show all steps c;early

Solve the following non homogeneous initial-Dirichlet problem in the unit sphere B1(u= u(r,t), r = |2|): 2. 0 0 Ut (Urr +Fur) = qe-t u(r,0) = U u(1,t) = 0 0. (4) (5) (6) 0 Hint: the solution is 2 2 u(r,t) = (-1)" -sin(^nr) In -> [l--e-480) Ue**] n=1 where in = n. Solve the following non homogeneous initial-Dirichlet problem in the unit sphere B1(u= u(r,t), r = |2|): 2. 0 0 Ut (Urr +Fur) = qe-t u(r,0) = U u(1,t) = 0 0. (4) (5) (6) 0 Hint: the solution is 2 2 u(r,t) = (-1)" -sin(^nr) In -> [l--e-480) Ue**] n=1 where in = n