Thread: solve the differential equation by undetermined coefficients

y'''-3y''+3y'-y=x-4e^x

ok so i found the roots of the equation where m = 1 and then i got my yc equation which was also pretty straight forward.

what i am having problems with is the yp equation,

i made my guess to be: Ax + Bx^3e^x <--- my book said i was wrong?

any help would be appreciated...

Originally Posted by slapmaxwell1

y'''-3y''+3y'-y=x-4e^x

ok so i found the roots of the equation where m = 1 and then i got my yc equation which was also pretty straight forward.

what i am having problems with is the yp equation,

i made my guess to be: Ax + Bx^3e^x <--- my book said i was wrong?

any help would be appreciated...

I think it should be just

Originally Posted by dwsmith

I think it should be just

When you plug that into the LHS, the operator will annihilate the exponential, so there's no way you'll get the RHS out of that. Because the root m = 1 has multiplicity 3, your particular solution will have to look something like slapmaxwell1's candidate. I might recommend have something more like



That might be overkill, but it might not. A hunch: any of those constant that are superfluous will be easy to solve for, I think. So I don't think you'll waste too much time doing it this way.