How to Solve a Nonhomogeneous 2nd Order DE with a Constant Term?

[Sean77771]

Homework Statement

y'' + 9y = 2x²e^3x + 5

Homework Equations

N/A

The Attempt at a Solution

I think the complementary solution y_c = c₁cos(3x) + c₂sin(3x).

If not for that little +5 at the end of the right hand side, I'm pretty sure I could solve it. But I don't know how to include it in my solution.

 

[HallsofIvy]

Try adding a constant to your specific solution.