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!
In part A I am not sure how to verify that the analytic solution is of the form described?
To verify the solution, just apply the Laplace operator to it and see that it gives 0 indeed. Note that your solution is separable , which should ease the procedure.
Originally Posted by helpthanks
Additionally I have done Laplace's transforms before but i have no idea how to do part B as well.
No need for Laplace transforms. This is the Laplace equation.
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!
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.