Differential Equation Problem: Undetermined Coefficient

Question

Determine the specific solution of the following initial-value problems. Use the method of undetermined coefficients to find the particular solution.

y'' - 2y' + 2y = x³ - 5, y(0)=6 and y'(0)=0

Note: so the general form is y=e^x(C1cos(x) + C2sin(x)) and I assume Yp = Ax³ -B? Is this the right guess? Or does it have to be Yp = Ax³ + Bx² + Cx -5? and for the initial value, do I have to plug them in to the Yp's?

Answer 1

The general solution looks good, but you have to look for a particular solution in the form

Yp(x) = Ax³ + Bx² + Cx +D. (not -5 instead of D).

It seems to me that you are making progress. Good luck.