Question

This is my equation for a non homogeneous equation: y"-2y'-3y=3e^2x

Answer 1

Solve the homogeneous equation using\[y=e^{\lambda x}\]to get a characteristic equation. Solve for lambda and your solution to that part will be \[y=c_1e^{\lambda_1 x}+c_2e^{\lambda_2 x}\]Then try a particular solution of the form Ae^(2x) or so...you can play around with it.

Can't spend much time on it - sorry. I'll check back later if I have time.