yesterday Fay ysinxtx2e7y F FEM M 3xytyt Xd Ffg N x'try MGM N x g Fg Ttp deck if My _Nx y g h 145 3 1 2 exactness N 2xty My 4 Nx This equation is not exactly DONE this method will not work to find the solution
yesterdayFayysinxtx2e7y
FFEM
M 3xytyt Xd FfgN x'try MGM N xg Fg
Ttp deck if My_Nxy g
h
1453 12 exactness
N 2xtyMy4 Nx
Thisequation is not exactlyDONEthismethod will notwork tofind thesolution
14 4 5 tKx'sµ 2 222g 7 3 4 3 7 3
check My NxMy 4x2gTHE 8xyttextNx 4g2 7.3 2 8xy 21
2
Its exactif My Nx11 21
Ourequation is
4xy 2k2g 2 22y 73y o
14 4 92 21x'yN 2 72y 7
3
we knowits exact fromabove
TEI S4 5 21 3 d treat antphi fee
FCxis 4g 21 lotsF xn 2 3,2 7x3y tolls
STEPI Fy 2x 7 370 S
set Fy N
4x2y 7 3to G 4 3 7 3
flood fo10G C
FG 9 2 292 7 3
general solution
2 242 73 C
Modelingfassumeamonthis30days
15.30 450micepermonth
dependsonpopulationdependsontheinitialpopulationIstheamountaddedbyreproduction more or lessthantheamountkilledby predation
Twoscenarios i Howmanymiceafter1month ifthestartingpopulationis
A P o 600 miceaddedbyreproduction 300Killedbyowls 450totalafter I wonthe6001300 450 450
B pfo 1000 micereproduction 500Killedbyoils 450total 1000 tSOO 450 1050
y 9 92 Goal y fsexy
y 9 4yd2xy
y 924 22
5fat 2
y EHI't2STEP1 lety xSteps Guess y ay
y
u.it a X
substitutewww.fs i the
separatevariablesu u
Wxe Itu1Zu u4 U'x Is4tu 4
Uk IttadividebyTudx dx
9 4 In Htcsitmplify uHiplytopandboltonby24
g2 u'd
ftp.tdxU b l Il l legate
Use substitution to integrate1etw 9t2udw4uduTuzdw
udufsuISZ.tdw
If IdwII Hth 19124 _In Htcsolvefor uIn191244 241 1 1 2C
elnl9t2u4 flak 1 2C
191244 e2klxlt2c
19they Kek
19ttuy ehlxY.ec
9t2u4 lx4e2cnInegafiu.x2T'isnonnegative so 1 4 12
9t2u2 eng g
2a2 x eh 9T 2
I 2
42 12 22e IzU FEE
y ax
5 IEEE X
theproblem asks for yd so lets squnboth
Y
asides
y f FEE x2
y x'e E xd
y2 Ex9ek_E