What is your question?
In part A I am not sure how to verify that the analytic solution is of the form described? Additionally I have done Laplace's transforms before but i have no idea how to do part B as well. Thanks for all your help!
Would you mind doing or starting this problem for me, i have quite a few like this i have to do but am having trouble going through the whole process of one problem. Thanks again!
Attached is my work so far.
You fixed and such that the boundary conditions are satisfied. Good. But you need to check that the solution satisfies the Laplace equation, i.e. .
The first page is where i verified that it is equal to zero and the second page I solved for A & B. What should i do differently on the first page that i did not do to show it is equal to zero?
On the first page you checked that the Dirichlet boundary conditions and . This shows that 2 boundary conditions are satisfied. You need to compute the Laplacian of the function to show that the equation is true everywhere in the domain.