Question

Please also help with this second order DE: y''+2y"-3y=e^3x

Answer 1

Do you mean \[ y^{\prime\prime}+2y^\prime-3y=e^{3x} \] ?

Answer 2

Hint: this has constant coefficients, there is a straight forward way of solving those. First solve the homogenous problem!
\[ y \left( x \right) ={C_1{\rm e}^{-3\,x}}+C_2{{\rm e}^{x}}+1/12\,{{\rm e}^{3\,x}} \]
That is your general solution.