Could you please solve this question, thanks!

Problem: Consider the equation Consider the heat equation du at atyu, 00, subject to the boundary conditions u(0, t) = u( L, t) = 0. Suppose 5TI u(r, 0) = 3sin - 8 sin L L where y is a positive constant. a) Use separation of variables to solve the problem. b) Evaluate lim u(x, t). 1-+00 Does the value of the constant y play a role in this limit? Explain