Answer Happy

Please provide formula used & step of solutions.
4. 5. By using separation of variables, show that the solution for the follow- ing heat equation with mixed boundary condition is given by u(x, t) = ди Ət əx²¹ u(0, t) = 0, u(a,0)=1, n=1 (2n-1) u(t,0)= 0<x< 1, t> 0, ur(1.t) = 0, t> 0, 0<x< 1, Consider the following heat equation du d'u Ət dr²¹ uz(0,t)=0, = sin sin (2n-1)πx (2n-11²+²t 2 0≤x≤ 40, t> 0, uz(40,t)=0, t>0, 0 < x < 1. TI 40 Find the solution u(x, t) using the method of separation of variables by setting u(x, t) = X(r)T(t).