Get a solution to the following partial differential equation?

Questions
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1

Dear All,
The following function J(t,x) and A given below, solve a partial differential equation given in the attached “problem.nb”. However, when I use DSolve, it does not get me anywhere. Can you please let me know how to get the solution in Mathematica? Many thanks.

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problem.nb (6.58 KB)

2

DSolve[]'s support for PDE equations is still somewhat limited,so don’t be surprised if some things don’t work yet.

See this

Regards M.I.

problem ver2.nb (10.1 KB)

3

Thank you.