5. Use the substitution u(x, t) = X(x) T (t) and separation of variables to solve the partial differential equation Ut1 = Ux No boundary conditions are given. Take the separation constant as a, Use...

Extracted text: 5. Use the substitution u(x, t) = X(x) T (t) and separation of variables to solve the partial differential equation Ut1 = Ux 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.