So here Use an eigenvalue-eigenfunction expansion to solve the BVP for the wave equation Ju Op...

   

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So here Use an eigenvalue-eigenfunction expansion to solve the BVP for the wave equation Ju Op (x,t) Ju 2 (x,t), 0 < <1, t> 0 u(0,t) = 0, u(1,t) = 0, t> 0, u(x, 0) = 0, u(x, 0) = x, 0 < < 1. =U u(x,t) an cos(nat) + b sin(nat)]on(x) n=1 where a and b, are generalized Fourier coefficients and phi,(x) are orthonormal eigenfunctions. an= bn = u(x,t) = n-1 So here Use an eigenvalue-eigenfunction expansion to solve the BVP for the wave equation Ju Op (x,t) Ju 2 (x,t), 0 < <1, t> 0 u(0,t) = 0, u(1,t) = 0, t> 0, u(x, 0) = 0, u(x, 0) = x, 0 < < 1. =U u(x,t) an cos(nat) + b sin(nat)]on(x) n=1 where a and b, are generalized Fourier coefficients and phi,(x) are orthonormal eigenfunctions. an= bn = u(x,t) = n-1