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Question

With u=u(x,t), solve the IBVP for the wave equation with homogeneous

Neumann boundary conditions for t>0 and 0<x<pi using Fourier Series:

(d^2/dt^2)u(x,t)-(d^2/dx^2)u(x,t)=0
(d/dt)u(x,0)=x^2
(d/dx)u(0,t)=0
(d/dx)u(pi,t)=0

where (d^2/dt^2) denotes the second derivative with respect to time and
(d^2/dx^2) denotes the second derivative with respect to space

Note: I'm pretty sure the solution begins with starting with a Fourier cosine series for u(x,t) and finding the cosine series for x^2 but I need to check this

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Subject: Math

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