Differential Equation: Finding the Particular Solution for 4y'-4y=x*e^(3x)

[nns91]

Homework Statement

4y'-4y=x*e^(3x)

Homework Equations

None

The Attempt at a Solution

The question is to find the particular solution

So I kinda know the way to solve this thing but the point is the start. I cannot figure out what will I set my y equal to. if it's only e^(3x) I will set my y=A*x*e^3x then find y' and substitute in the original equation to find the particular solution.

 

[lurflurf]

4y'-4y=x*e^(3x)
4(D-1)y=x*e^(3x)
4(D-3)^2(D-1)y=0
solve
4(D-3)^2(D-1)y=0
then eliminate the extraneous solutions of

4(D-1)y=x*e^(3x)