Use the method of eigenfunctions expansion to solve the heat equation

?u =9?2u, 00, ?t ?x2

subject to the time dependent non-homogeneous boundary conditions

?u(0,t) = 0, ?u(?,t) = cost, t > 0,

?x

and the initial condition

?x

u(x,0)=0, 0

Problem 1 . 25 Use the method of eigen functions expansion to solve the heat equation On 8 21 are OCOST 120 subject to the time dependent non- homogeneous boundary conditions Ju 20 ( 0 , t ) = 0 du air ( T t ) = cost , 120 and the initial condition 2 ( 1 0 ) = 0 0COST Him First construct , function in I t ) that satisfies the PDC day 20 3 ( 2 1 ) = 0 together with the given boundary conditions