Question

Solve the following initial/boundary value problem: ∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π, u(t,0)=u(t,π)=0 for t>0, u(0,x)=sin^2x...

Solve the following initial/boundary value problem:

∂u(t,x)/∂t = ∂^2u(t,x)/∂x^2 for t>0, 0<x<π,

u(t,0)=u(t,π)=0 for t>0,

u(0,x)=sin^2x for 0≤x≤ π.

if you like, you can use/cite the solution of Fourier sine series of sin^2(x) on [0,pi] = 1/4-(1/4)cos(2x)

please show all steps and work clearly so I can follow your logic and learn to solve similar ones myself.

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Doubt in any step then comment below.. i will explain you.

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