Similar to Example 1, the following is a solution for . For now, is not considered.
This time, pdsolve computes a complete (that is, not the most general) solution using separation of variables. The solution appears in terms of arbitrary constants and the separation variable .
The integration constants can be redefined to absorb
Now, evaluate the solution at and and impose the given boundary conditions to build a system (e1 and e2, so two equations) to be solved for these three constants.
Solve for the constants.
The first solution above leads to a solution of no interest: . The second solution above is the one we want.
Here pdetest verifies the answer for pde[2] and the first boundary condition, but fails with the second one.
However, the answer computed is correct. The second boundary condition can be constructed by evaluating the answer at . This task can be performed within pdetest.