Inhomogeneous wave equation help

[finmath]

I need help solving 3Utt+10Uxt+3Uxx=sin(x+t)

I have found the homogeneous part, which is U(x,t)=f(3x-t) +g(x-3t), but I don't know where to go from there. Any help would be much appreciated!

 

[arildno]

Well, make a trial solution $$U_{p}(x,t)=A\sin(x+t)$$ and see if you can determine what "A" must be.

 

[finmath]

Back to the basics! For some reason I thought it was going to be way more difficult.
My final solution is U(x,t)=f(3x-t) + g(x-3t) - sin(x+t)/16

Thanks for your help!

 

[matematikawan]

Well, make a trial solution $$U_{p}(x,t)=A\sin(x+t)$$ and see if you can determine what "A" must be.

I though the try function should be of the form

$$U_{p}(x,t)=A\sin(x+t) + B\cos(x+t)$$

 

[arildno]

And B will be 0..