- #1
bennyska
- 112
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Homework Statement
y'' + y = sin x + x*cos x
Homework Equations
The Attempt at a Solution
i don't like undetermined coefficients. so far, for me, it's been so much trial and error, although i am getting a little faster at it.
anyway, i didn't work out the homogeneous equation, but i can see it'll be something with complex roots. i worked out the part for sin x and got yp=-1/2*x*cos x.
now, with x*cos x, i tried a*x2sin x + b*x2cos x.
when i plug all this into the original equation, i get
(4ax + 2b) cos x + (2a+4bx)sin x. so, i think i need to get 4ax + 2b = x, and 2a+4bx=0, right? i don't see any other way than to let 4a =1, and 2b=0, but this doesn't work in getting 2a+4bx=0. am i making some dumb mistake?