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Solve the following inhomogeneous wave problem for a vibrating string of length 1 (0 ≤ x...

Solve the following inhomogeneous wave problem for a vibrating string of length 1 (0 ≤ x ≤ 1):

∂^2u/ ∂t^2 = 1/2 * ∂^2u/∂x^2 − x.

The initial conditions are u(x, 0) = cos(πx/2) + 1/3x^3 & ∂u/∂t (x, 0) = 0

boundary conditions are ∂u/∂x(0, t) = 0  & u(1, t) = 1/3.

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