Finding the particular solution of DE

[overseastar]

I have a nonhomogeneous DE and wants to find the particular solution for Asin(x)sin(t)

Is there any tips in using method of undetermined coefficient to guess the particular solution of this?

[HallsofIvy]

Is this a partial differential equation or is one of x and t the dependent variable so that you have a nonlinear equation? In either case "undetermined coefficients" doesn't apply here.

[overseastar]

the question is asking us to solve this nonhomogeneous problem:

Utt = Uxx + sin(x)sint(t)

and I think in one step of the calculations, we need to find the general solution of sin(x)sin(t) along with the particular solution.

Or is there another way to approach this question?

[masudr]

Stipulate that U(x,t)=X(x)T(t). Then you can separate into 2 ODEs.

[overseastar]

Sorry, I guess I should be more specified.
It asked us to use the Fourier Series Method.