I'm out of college and am brushing up on Laplace Transforms. I have a problem I've solved, but I believe the solution I got is wrong and can't find my error.(adsbygoogle = window.adsbygoogle || []).push({});

The problem is 2x''-x'=t*sin(t) x(0)=5,x'(0)=3

My solution...

Take the Laplace Transform

2(s^2x-5s-3)-(sx-5)=2s/(s^2+1)^2

Rearranging, I get

x(2s^2-s)-10s-1=2s/(s^2+1)^2

Solve for x

x=(10s+1)/(2s^2-s)+2/((2s-1)(s^2+1)^2

Then, doing a PFD on the first term, I get -1/s+8/(2s-1)

Doing an inverse Laplace Transform, I get x(t)=-1+8e^(t/2)+Integral((sin(y)-ycos(y)(e^(1/2)((t-y))dy,0,y)

I used the convolution theorem on the second term on the RHS. That doesn't look right because the initial conditions aren't satisfied. Can anyone point me in the right direction?

Thanks!

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# ODE Review

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