Please show clear and legible work along with explanation on how to solve this p

Question

Please show clear and legible work along with explanation on how to solve this problem.

Solve by nonhomogenous boundary condition methods:

u_ xx= u_tt-10, 0<x<1,    t>0

Boundary Conditions:    u(0,t) = 2       u_x(1,t) = 0

Initial Conditions:           u(x,0)= 2       u_t(x,0)= sin((3pix)/2)

Yes, those are partial derivatives. I just an underscore instead of inserting an equation. Read how it is and you should be able to comprehend the problem. I have the solution to this problem, but I do not know how to approach. Will award exra time and points. If you have any questions, please let me know.

Explanation / Answer

u_ xx= u_tt-10......................(1)

U(x,t) = X(x) T(t)

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