Page | 1 BAB I PENDAHULUAN 1.1 Latar Belakang Di dalam mata kuliah matematika III terdapat bab yang menjelaskan mengenai Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan. Dalam rangka memenuhi proyek akhir mata kuliah matematika III maka dibuatlah suatu aplikasi untuk memenuhi penyelesaian beberapa persoalan matematika yang secara khusus mengenai bab Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan. Software yang kami gunakan dalam pembuatan aplikasi ini adalah Matlab R2009a Student. Algoritma yang telah kami rancang lalu kami aplikasikan pada program Matlab, kemudian di uji cobakan dengan membandingkan antara hasil perhitungan manual dengan hasil dari output program aplikasi ini sehingga terdapat kesesuaian hasil yang sama dan valid. Dengan adanya aplikasi ini maka diharapkan untuk menyelesaikan permasalahan matematika, khususnya Persamaan Diferensial Linier Tidak Homogen Orde n Koefisien Konstan dapat dengan lebih cepat, mudah, dan akurat bagi pengguna aplikasi ini. Para pengguna aplikasi ini diharapkan dapat mengerti juga cara membuat program ini. Adapun aplikasi ini dapat dijadikan pembanding untuk mengkalibrasi hasil perhitungan manual dengan perhitungan hasil operasi program dari aplikasi Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan. 1.2 Perumusan Masalah 1. Apakah tujuan dari pembuatan aplikasi ini? 2. Apa Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan? 3. Bagaimana kaidah atau perumusan dalam Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan? 4. Bagaimana contoh penyelesaian soal dalam Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan? 5. Bagaimana pengaplikasian dalam Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan?
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BAB I
PENDAHULUAN
1.1 Latar Belakang
Di dalam mata kuliah matematika III terdapat bab yang menjelaskan mengenai
Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan.
Dalam rangka memenuhi proyek akhir mata kuliah matematika III maka dibuatlah
suatu aplikasi untuk memenuhi penyelesaian beberapa persoalan matematika yang secara
khusus mengenai bab Persamaan Diferensial Linier Tidak Homogen Orde n dengan
Koefisien Konstan. Software yang kami gunakan dalam pembuatan aplikasi ini adalah
Matlab R2009a Student. Algoritma yang telah kami rancang lalu kami aplikasikan pada
program Matlab, kemudian di uji cobakan dengan membandingkan antara hasil perhitungan
manual dengan hasil dari output program aplikasi ini sehingga terdapat kesesuaian hasil yang
sama dan valid.
Dengan adanya aplikasi ini maka diharapkan untuk menyelesaikan permasalahan
matematika, khususnya Persamaan Diferensial Linier Tidak Homogen Orde n Koefisien
Konstan dapat dengan lebih cepat, mudah, dan akurat bagi pengguna aplikasi ini. Para
pengguna aplikasi ini diharapkan dapat mengerti juga cara membuat program ini. Adapun
aplikasi ini dapat dijadikan pembanding untuk mengkalibrasi hasil perhitungan manual
dengan perhitungan hasil operasi program dari aplikasi Persamaan Diferensial Linier Tidak
Homogen Orde n dengan Koefisien Konstan.
1.2 Perumusan Masalah
1. Apakah tujuan dari pembuatan aplikasi ini?
2. Apa Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien Konstan?
3. Bagaimana kaidah atau perumusan dalam Persamaan Diferensial Linier Tidak Homogen
Orde n dengan Koefisien Konstan?
4. Bagaimana contoh penyelesaian soal dalam Persamaan Diferensial Linier Tidak
Homogen Orde n dengan Koefisien Konstan?
5. Bagaimana pengaplikasian dalam Persamaan Diferensial Linier Tidak Homogen Orde n
dengan Koefisien Konstan?
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6. Bagaimana program berjalan dalam menyelesaikan soal Persamaan Diferensial Linier
Tidak Homogen Orde n dengan Koefisien Konstan?
7. Apakah penyajian dari aplikasi ini sudah memudahkan dan membantu pengguna dalam
menyelesaikan Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien
Konstan?
8. Apakah aplikasi ini dapat dijadikan acuan tetap atau hanya sebatas media pembanding
antara perhitungan manual dengan perhitungan program?
1.3 Tujuan
1. Tujuan dalam pembuatan aplikasi ini adalah untuk membantu mahasiswa menyelesaikan
soal mengenai Persamaan Diferensial Linier Tidak Homogen Orde n dengan Koefisien
Konstan dengan mudah menggunakan program bantuan Matlab R2009a Student .
2. Menyajikan aplikasi Persamaan Diferensial Linier Tidak Homogen Orde n dengan
Koefisien Konstan dengan penggunaan yang mudah dan cepat.
3. Sebagai acuan tetap pembantu perhitungan atau sebagai media pembanding antara hasil
perhitungan manual dengan output perhitungan program aplikasi yang dibuat.
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BAB II
PEMBAHASAN
2.1 Persamaan Diferensial Linear Tidak Homogen dengan Koefien Konstan (PDLTH)
Menjumlah Hasil Persamaan Homogen dengan Hasil Istimewa
Dalam gejala transien atau peralihan kapasitor dalam rangkaian bekerja menyimpan
energi listrik yang terhubung dengan tegangan bolak balik (AC). Ketika muatan dalam
kapasitor penuh maka kapasitor akan mengalami keadaan yang biasa disebut dengan keadaan
stasioner. Untuk lebih jelasnya perhatikan gambar berikut ini:
Dimana pada tegangan sumber (VS) atau tegangan bolak balik (VAC) pada gambar di atas
dituliskan dalam persamaan :
π½ = π½π πππ (π + )
Maka persamaan untuk mencari tegangan rangkaiannya dapat kita cari dengan menjumlahkan
tegangan pada kapasitor dan tegangan pada resistor sehingga kita dapat menuliskan;
π=β
ππ +
βππΆ
π = πΌ. π +π
πΆ
πΌ. π +π
πΆ= π0sin (ππ‘ + )
Untuk menyesaikan persamaan diatas dapat menggunakan βPersamaan Deferensial Derajat
Satu yang Tidak Homogenβ. Sehingga untuk mencari hasil persamaan rangkaian RC diatas,
ada beberapa langkah yang harus kita lakukan seperti menyelesaikan persoalan PDLTH,
yaitu:
Hasil Persamaan Homogen
Hasil Istimewa
Menjumlah Hasil Persamaan Homogen dengan Hasil Istimewa
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2. 5 Algoritma Program
Mulai
Tampilan depan dengan judul βPersamaan Differensial Linier Tidak Homogenβ
Masuk ke Latihan Soal
Masukan soal dari Persamaan Differensial Linier Tidak Homogen (PDLTH):
ΓΈ(y) = f(x) dimana f(x) berupa Aljabar, Eksponensial atau Trigonometri
Masukan fungsi ΓΈ(y) = 0 untuk mencari jawab homogennya.
Masukan konstanta dari persamaan karakteristik.
Proses :
roots(f) : untuk mencari hasil akar- akar karakteristik dimana f adalah masukan
dari koefisien persamaan karakteristik
dsolve(d) : untuk mencari jawab homogen dimana d adalah masukan dari fungsi
ΓΈ(y) = 0
dsolve(b) : untuk mencari jawab umum dimana b adalah masukan dari soal
PDLTH
g = d β b : untuk mencari jawab khusus
clear : untuk mereset kembali suatu perhitungan
Hasil program akan mencetak akar- akar persamaan, jawaban homogen dan jawaban
umum, dan jawab khusus.
Selesai
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2.6 Flowchart Program
MULAI
INPUT
ΓΈ(y) = f(x) : Aljabar, Eksponen, Trigonometri
INPUT
ΓΈ(x) = 0 : Aljabar, Eksponen, Trigonometri
INPUT
Koefisien PK
OUTPUT
? Akar-Akar Persamaan
Proses
Roots()
OUTPUT
? Jawaban Homogen
Proses
Dsolve()
OUTPUT
? Jawaban Umum
SELESAI
Proses
Jawab Khusus = Jawab Umum β Jawab Homogen
Proses
Dsolve()
OUTPUT
? Jawaban Khusus
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2. 7 List Program
Tampilan Depan
function varargout = cover(varargin) % COVER M-file for cover.fig % COVER, by itself, creates a new COVER or raises the existing % singleton*. % % H = COVER returns the handle to a new COVER or the handle to % the existing singleton*. % % COVER('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in COVER.M with the given input arguments. % % COVER('Property','Value',...) creates a new COVER or raises the % existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before cover_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to cover_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help cover
% Last Modified by GUIDE v2.5 06-Dec-2014 15:27:54
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @cover_OpeningFcn, ... 'gui_OutputFcn', @cover_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before cover is made visible. function cover_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to cover (see VARARGIN)
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% Choose default command line output for cover handles.output = hObject;
% Update handles structure guidata(hObject, handles); axes(handles.axes1); image(imread('cover','png')); grid off axis off
% UIWAIT makes cover wait for user response (see UIRESUME) % uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line. function varargout = cover_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
% --- Executes on button press in pushbutton1. function pushbutton1_Callback(hObject, eventdata, handles) % hObject handle to pushbutton1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run untitled
Tampilan Latihan Soal
function varargout = untitled(varargin) % UNTITLED M-file for untitled.fig % UNTITLED, by itself, creates a new UNTITLED or raises the existing % singleton*. % % H = UNTITLED returns the handle to a new UNTITLED or the handle to % the existing singleton*. % % UNTITLED('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in UNTITLED.M with the given input
arguments. % % UNTITLED('Property','Value',...) creates a new UNTITLED or raises
the % existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before untitled_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to untitled_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)".
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% % See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help untitled
% Last Modified by GUIDE v2.5 09-Dec-2014 19:09:16
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @untitled_OpeningFcn, ... 'gui_OutputFcn', @untitled_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before untitled is made visible. function untitled_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to untitled (see VARARGIN)
% Choose default command line output for untitled handles.output = hObject;
% Update handles structure guidata(hObject, handles); axes(handles.axes1); image(imread('gambar','png')); grid off axis off
% UIWAIT makes untitled wait for user response (see UIRESUME) % uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line. function varargout = untitled_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
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function masuk_Callback(hObject, eventdata, handles) % hObject handle to masuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of masuk as text % str2double(get(hObject,'String')) returns contents of masuk as a
double
% --- Executes during object creation, after setting all properties. function masuk_CreateFcn(hObject, eventdata, handles) % hObject handle to masuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
% --- Executes on button press in tekan. function tekan_Callback(hObject, eventdata, handles) % hObject handle to tekan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) c=get(handles.masuk,'string') c=str2mat(c) d=dsolve(c) d=subs(d,'t','x') d=subs(d,'C2','C1') d=subs(d,'C3','C2') d=subs(d,'C4','C3') d=subs(d,'C5','C4') d=subs(d,'C6','C5') d=str2mat(d) d=mat2str(d) set(handles.keluar,'string',d)
function keluar_Callback(hObject, eventdata, handles) % hObject handle to keluar (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
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% Hints: get(hObject,'String') returns contents of keluar as text % str2double(get(hObject,'String')) returns contents of keluar as a
double
% --- Executes during object creation, after setting all properties. function keluar_CreateFcn(hObject, eventdata, handles) % hObject handle to keluar (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
% --- If Enable == 'on', executes on mouse press in 5 pixel border. % --- Otherwise, executes on mouse press in 5 pixel border or over text2. function text2_ButtonDownFcn(hObject, eventdata, handles) % hObject handle to text2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% --- Executes during object deletion, before destroying properties. function text2_DeleteFcn(hObject, eventdata, handles) % hObject handle to text2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
function akar_Callback(hObject, eventdata, handles) % hObject handle to akar (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of akar as text % str2double(get(hObject,'String')) returns contents of akar as a
double
% --- Executes during object creation, after setting all properties. function akar_CreateFcn(hObject, eventdata, handles) % hObject handle to akar (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
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% --- Executes on button press in pushbutton2. function pushbutton2_Callback(hObject, eventdata, handles) % hObject handle to pushbutton2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) b=get(handles.akhir,'string') d=get(handles.keluar,'string') syms C1 syms C2 syms C3 syms C4 syms C5 syms C6 syms C7 syms t syms x g=sym(b)-sym(d) j=str2mat(g) set(handles.khusus,'string',j)
% -------------------------------------------------------------------- function menu_Callback(hObject, eventdata, handles) % hObject handle to menu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close; run cover
function persamaan_Callback(hObject, eventdata, handles) % hObject handle to persamaan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of persamaan as text % str2double(get(hObject,'String')) returns contents of persamaan as
a double
% --- Executes during object creation, after setting all properties. function persamaan_CreateFcn(hObject, eventdata, handles) % hObject handle to persamaan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
% --- Executes on button press in pushbutton3. function pushbutton3_Callback(hObject, eventdata, handles)
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% hObject handle to pushbutton3 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) a=get(handles.awal,'string') a=subs(a,'x','t') a=str2mat(a) b=dsolve(a) b=subs(b,'t','x') b=subs(b,'C2','C1') b=subs(b,'C3','C2') b=subs(b,'C4','C3') b=subs(b,'C5','C4') b=subs(b,'C6','C5') b=str2mat(b) b=mat2str(b) set(handles.akhir,'string',b)
function awal_Callback(hObject, eventdata, handles) % hObject handle to awal (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of awal as text % str2double(get(hObject,'String')) returns contents of awal as a
double
% --- Executes during object creation, after setting all properties. function awal_CreateFcn(hObject, eventdata, handles) % hObject handle to awal (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
function akhir_Callback(hObject, eventdata, handles) % hObject handle to akhir (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of akhir as text % str2double(get(hObject,'String')) returns contents of akhir as a
double
% --- Executes during object creation, after setting all properties. function akhir_CreateFcn(hObject, eventdata, handles) % hObject handle to akhir (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
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% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
% -------------------------------------------------------------------- function petunjuk_Callback(hObject, eventdata, handles) % hObject handle to petunjuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run petunjuk
% -------------------------------------------------------------------- function tentang_Callback(hObject, eventdata, handles) % hObject handle to tentang (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close; run tentang
function khusus_Callback(hObject, eventdata, handles) % hObject handle to khusus (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of khusus as text % str2double(get(hObject,'String')) returns contents of khusus as a
double
% --- Executes during object creation, after setting all properties. function khusus_CreateFcn(hObject, eventdata, handles) % hObject handle to khusus (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called
% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'),
get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end
% --- Executes on button press in hapus. function hapus_Callback(hObject, eventdata, handles) % hObject handle to hapus (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) set(handles.keluar,'string','') set(handles.khusus,'string','') set(handles.akar,'string','')
% --- Executes on button press in clear. function clear_Callback(hObject, eventdata, handles) % hObject handle to clear (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) clear all clc
% -------------------------------------------------------------------- function flowchart_Callback(hObject, eventdata, handles) % hObject handle to flowchart (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run flowchart
% -------------------------------------------------------------------- function materi_Callback(hObject, eventdata, handles) % hObject handle to materi (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run materi
Tampilan Petunjuk
function varargout = petunjuk(varargin) % PETUNJUK M-file for petunjuk.fig % PETUNJUK, by itself, creates a new PETUNJUK or raises the existing % singleton*. % % H = PETUNJUK returns the handle to a new PETUNJUK or the handle to % the existing singleton*. % % PETUNJUK('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in PETUNJUK.M with the given input
arguments. % % PETUNJUK('Property','Value',...) creates a new PETUNJUK or raises
the % existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before petunjuk_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to petunjuk_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES
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% Edit the above text to modify the response to help petunjuk
% Last Modified by GUIDE v2.5 09-Dec-2014 20:18:28
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @petunjuk_OpeningFcn, ... 'gui_OutputFcn', @petunjuk_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before petunjuk is made visible. function petunjuk_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to petunjuk (see VARARGIN)
% Choose default command line output for petunjuk handles.output = hObject;
% Update handles structure guidata(hObject, handles); axes(handles.axes1); image(imread('petunjuk','png')); grid off axis off
% UIWAIT makes petunjuk wait for user response (see UIRESUME) % uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line. function varargout = petunjuk_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
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% -------------------------------------------------------------------- function menu_Callback(hObject, eventdata, handles) % hObject handle to menu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run cover
% -------------------------------------------------------------------- function latihan_Callback(hObject, eventdata, handles) % hObject handle to latihan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run untitled
% -------------------------------------------------------------------- function tentang_Callback(hObject, eventdata, handles) % hObject handle to tentang (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run tentang
% -------------------------------------------------------------------- function flowchart_Callback(hObject, eventdata, handles) % hObject handle to flowchart (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run flowchart
% -------------------------------------------------------------------- function materi_Callback(hObject, eventdata, handles) % hObject handle to materi (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run materi
Tampilan Tentang
function varargout = tentang(varargin) % TENTANG M-file for tentang.fig % TENTANG, by itself, creates a new TENTANG or raises the existing % singleton*. % % H = TENTANG returns the handle to a new TENTANG or the handle to % the existing singleton*. % % TENTANG('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in TENTANG.M with the given input arguments. % % TENTANG('Property','Value',...) creates a new TENTANG or raises the
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% existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before tentang_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to tentang_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help tentang
% Last Modified by GUIDE v2.5 09-Dec-2014 19:10:08
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @tentang_OpeningFcn, ... 'gui_OutputFcn', @tentang_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before tentang is made visible. function tentang_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to tentang (see VARARGIN)
% Choose default command line output for tentang handles.output = hObject;
% Update handles structure guidata(hObject, handles); axes(handles.axes1); image(imread('tentang','png')); grid off axis off
% UIWAIT makes tentang wait for user response (see UIRESUME) % uiwait(handles.figure1);
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% --- Outputs from this function are returned to the command line. function varargout = tentang_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
% -------------------------------------------------------------------- function menu_Callback(hObject, eventdata, handles) % hObject handle to menu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close; run cover
% -------------------------------------------------------------------- function petunjuk_Callback(hObject, eventdata, handles) % hObject handle to petunjuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run petunjuk
% -------------------------------------------------------------------- function latihan_Callback(hObject, eventdata, handles) % hObject handle to latihan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close; run untitled
% -------------------------------------------------------------------- function flowchart_Callback(hObject, eventdata, handles) % hObject handle to flowchart (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run flowchart
% -------------------------------------------------------------------- function materi_Callback(hObject, eventdata, handles) % hObject handle to materi (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run materi
Tampilan Flowchart
function varargout = flowchart(varargin)
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% LATIHAN M-file for latihan.fig % LATIHAN, by itself, creates a new LATIHAN or raises the existing % singleton*. % % H = LATIHAN returns the handle to a new LATIHAN or the handle to % the existing singleton*. % % LATIHAN('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in LATIHAN.M with the given input arguments. % % LATIHAN('Property','Value',...) creates a new LATIHAN or raises the % existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before flowchart_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to flowchart_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help latihan
% Last Modified by GUIDE v2.5 09-Dec-2014 19:10:56
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @flowchart_OpeningFcn, ... 'gui_OutputFcn', @flowchart_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before latihan is made visible. function flowchart_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to latihan (see VARARGIN)
% Choose default command line output for latihan handles.output = hObject;
axes(handles.axes1); image(imread('flow','png')); grid off axis off
% UIWAIT makes latihan wait for user response (see UIRESUME) % uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line. function varargout = flowchart_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
% -------------------------------------------------------------------- function menu_Callback(hObject, eventdata, handles) % hObject handle to menu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run cover
% -------------------------------------------------------------------- function petunjuk_Callback(hObject, eventdata, handles) % hObject handle to petunjuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run petunjuk
% -------------------------------------------------------------------- function tentang_Callback(hObject, eventdata, handles) % hObject handle to tentang (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run tentang
% -------------------------------------------------------------------- function latihan_Callback(hObject, eventdata, handles) % hObject handle to latihan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run untitled
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% -------------------------------------------------------------------- function materi_Callback(hObject, eventdata, handles) % hObject handle to materi (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run materi
Tampilan Materi
function varargout = materi(varargin) % MATERI M-file for materi.fig % MATERI, by itself, creates a new MATERI or raises the existing % singleton*. % % H = MATERI returns the handle to a new MATERI or the handle to % the existing singleton*. % % MATERI('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in MATERI.M with the given input arguments. % % MATERI('Property','Value',...) creates a new MATERI or raises the % existing singleton*. Starting from the left, property value pairs
are % applied to the GUI before materi_OpeningFcn gets called. An % unrecognized property name or invalid value makes property
application % stop. All inputs are passed to materi_OpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help materi
% Last Modified by GUIDE v2.5 09-Dec-2014 19:07:40
% Begin initialization code - DO NOT EDIT gui_Singleton = 1; gui_State = struct('gui_Name', mfilename, ... 'gui_Singleton', gui_Singleton, ... 'gui_OpeningFcn', @materi_OpeningFcn, ... 'gui_OutputFcn', @materi_OutputFcn, ... 'gui_LayoutFcn', [] , ... 'gui_Callback', []); if nargin && ischar(varargin{1}) gui_State.gui_Callback = str2func(varargin{1}); end
if nargout [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); else gui_mainfcn(gui_State, varargin{:}); end % End initialization code - DO NOT EDIT
% --- Executes just before materi is made visible.
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function materi_OpeningFcn(hObject, eventdata, handles, varargin) % This function has no output args, see OutputFcn. % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % varargin command line arguments to materi (see VARARGIN)
% Choose default command line output for materi handles.output = hObject;
% Update handles structure guidata(hObject, handles); axes(handles.axes1); image(imread('materi','png')); grid off axis off
% UIWAIT makes materi wait for user response (see UIRESUME) % uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line. function varargout = materi_OutputFcn(hObject, eventdata, handles) % varargout cell array for returning output args (see VARARGOUT); % hObject handle to figure % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure varargout{1} = handles.output;
% -------------------------------------------------------------------- function menu_Callback(hObject, eventdata, handles) % hObject handle to menu (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run cover
% -------------------------------------------------------------------- function petunjuk_Callback(hObject, eventdata, handles) % hObject handle to petunjuk (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run petunjuk
% -------------------------------------------------------------------- function tentang_Callback(hObject, eventdata, handles) % hObject handle to tentang (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run tentang
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% -------------------------------------------------------------------- function flowchart_Callback(hObject, eventdata, handles) % hObject handle to flowchart (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run flowchart
% -------------------------------------------------------------------- function latihan_Callback(hObject, eventdata, handles) % hObject handle to latihan (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close run untitled
2.8 Tampilan Program
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BAB III
PENUTUP
3.1 Rangkuman
Persamaan diferensial linier tidak homogen berbeda dengan persamaan differensial linier
homogen karena dalam PDLTH fungsi dari β (π¦) tidak bernilai 0 melaikan terdapat f(x).
Dimana bentuk PDLTH sebagai berikut:
π0
πππ¦
ππ₯π+ π1
ππβ1π¦
ππ₯πβ1+ β― + πππ¦ = π(π₯)
Atau
β (π¦) = π(π₯)
Sehingga untuk menyelesaikan PDLTH kita harus melakukan beberapa langkah, yaitu:
Mencari jawab homogen (yh) dimana β (π¦) = 0. Kemudian disubstitusikan dengan
π¦ = ππ‘π₯
Mencari jawab khusus (yk) dimana β (π¦) = π(π₯) β 0 dengan menggunakan fungsi
percobaan
Maka jawab umum :
π¦π’ = π¦β + π¦π
3.2 Kesimpulan
Demikianlah yang dapat kami sajikan kepada pembaca tentang laporan makalah
Persamaan Diferensial Linier Tidak Homogen. Dalam pengerjaan Makalah ini kami
menggunakan beberapa buku sebagai sumber serta referensi lainnya. Untuk pemograman
kami menggunakan software Matlab R2009a Student dalam penyelesaian Persamaan
Diferensial Linier Tidak Homogen. Makalah kami sajikan secara bertahap, mulai dari
pengenalan teori, contoh soal latihan, latihan soal, algoritma, Flow Chart, list program
dan hasil program, sehingga makalah ini dapat mempermudah pembaca dalam mengikuti
panduan penggunaan dari Program tersebut. Akhir kata, kami berharap mudah-mudahan
makalah kami dapat bermanfaat dan bakerja dengan optimal apabila digunakan. Saran
yang kami harapkan dari pembaca untuk pengembangan makalah dan program
kedepanya. Apabila diproyek dan dimakalah ini terdapat kesalahan kami mohon maaf
sebesar-besarnya.
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Daftar Pustaka
Kreyszig, Erwin. (1991). Matematika Teknik Lanjutan Jilid I. Jakarta: Penerbit Erlangga.
Rawuh, B. Kartasasmita, I Nyoman Susila.(1984). Kalkulus dan Geometri Analitis Jilid 2.
Jakarta: Penerbit Erlangga.
Riogilang, RH. (1979). Persamaan Diferensial. Bandung: Penerbit Bina Cipta.