1. The problem statement, all variables and given/known data du/dt=d2u/dx2, u(0,t)=0, u(pi,t)=0 u(x,0) = sin^2(x) 0<x<pi Find the solution Also find the solution to the initial condition: du/dt u(x,0) = sin^2(x) 0<x<pi 3. The attempt at a solution From separation of variables I obtain u(x,t) = B.e^(-L^2t).sin(Lx) For the boundary condition u(pi,t)=0, u(x,t) = Bm . e^(-m^2t) . sin(mx) Finally for u(x,0) = sin^2x u(x,0) = 4(cos(m.pi)-1).e^(-m^2t).sinmx / pi(m^3-4m) found through superposition and fourier sum of sines What I dont see is how to solve the initial condition because when I diff. above wrt t and set t-0 I obtain du/dt u(x,0) = -m^2 4(cos(m.pi)-1).e^(-m^2t).sinmx / pi(m^3-4m) = sin^2x How can this be set to sin^2x by choosing a value of m?