Find particular solution third order Diff Eq

[Herricane]

Homework Statement

y''' - y = e^x + 7

Homework Equations

The Attempt at a Solution

I used y=Ae^x +B and then I multiplied by x^2 because y_c = c1 + c2 e^x + c3 e^(-x)

the c1 and c2 e^x value repeat. Therefore I got: y= Ax^2 e^x + Bx^2

I got A = 0 and A=1 which is wrong and B=0

Any hints? do I need to add a Cx e^x and then multiply by x^2?

 

[rock.freak667]

Your auxiliary equation would be r^3-1=0 which would lead to only one real root and two imaginary roots.

Since e^x is on the right side, the particular integral for the e^x on the right would be xe^x.

You will need to change your complementary solution y_c to reflect one real root and two imaginary roots.