3. a. Solve the following initial boundary value problem for the heat equation ди 82 и = D 00 St дх2 u(x,0) = f(

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3. a. Solve the following initial boundary value problem for the heat equation ди 82 и = D 0<x<L, t>0 St дх2 u(x,0) = f(x) u(0,t) = u(L, t) = 0, t > 0, 9пх when f(x) = 6 sin L b. Solve the following initial boundary value problem for the diffusion equation ди at ди Әх D u(x,0) = f(x) ди дх when f(x) = дги до 2 (0, t) = , 0<x<L, t>0 (L,t) =0, t> 0, 0, x<L/2 1, x> L/2.