pls help solve this problem

6. [20 marks; (a) 12 marks (b) 4 marks (c) 4 marks] (a) Solve the homogeneous heat equation with homogeneous boundary condition: We(x, t) = Wex(x, t), 1 >0, 05x51 Wx (0, t) = 0, 1>0 W ( 7, t ) = 0, t>0 w(x, 0) = x(7 -x)