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Solve the IBVP for the heat equation.

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Solve the IBVP for the heat equation u_t = u_xx, 0 < x < pi, with Neumann boundary conditions u_x(0, t) = 1, u_x(pi, t) = 0, and initial condition u(x, 0) = 0.

Hint. reduce to homogenous boundary conditions by subtracting a function U(x) that satisfies U_x(0) = 1, U_x(pi) = 0.

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