5. Use the substitution u(x.r) = X(x) T(1) and separation of varlables to solve the partlal differential equation U, = ur No boundary conditions are given. Take the separation constant as -a. Use the...

Extracted text: 5. Use the substitution u(x.r) = X(x) T(1) and separation of varlables to solve the partlal differential equation U, = ur No boundary conditions are given. Take the separation constant as -a. Use the same methods used to determine the general solution to the heat equation as demonstrated in your notes and determine the most general solution in terms of a.