- #1

kq6up

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## Homework Statement

Find the specific solution for: y''-2y'+y=xe^x+4, y(0)=1, y'(0)=1.

## Homework Equations

N/A

## The Attempt at a Solution

Since xe^x is already in the general solution of the homogeneous version of this diff eq (complementary solution), my first guess for a partial solution term would be x^2e^x (xe^x is already taken by the complementary sol). However, it no worky. The correct guess is x^3e^x. I am not sure why this term has a higher power of x then the order of the DiffEq. I would have never have guessed this. Is there a reason I should have guessed this, or in general do I have to keep increasing powers until I find one that works? I am trying to find ways to save time on an exam.

Thanks,

Chris [/B]