Differences Between Linear and Nonlinear Equations

Differences Between Linear and Nonlinear Equations

Linear Differential Equations

Linear Differential Equations

Example: dy/dt = sin(t) y + t

Example: dy/dt = y/(1-t)

Theorem

Example

Nonlinear Differential Equation

Example: Non-Unique Solutions

Example: dy/dy=y^(1/3)

Example: Non-Unique Solutions

Example: Hidden Discontinuities

Example: dy/dt = y^2

Example: Incomplete General Solution

Example: Implicit Solutions

Example: dy/dt = tan(t) y/(1+y)

Theorem

Example