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Solve the following heat equation dt = u dx +x, t> 0, 0 < x < 1 u(t,0) = 1, u(t, 1) = -1,

Solve the following heat equation dt = u dx +x, t> 0, 0 < x < 1 u(t,0) = 1, u(t, 1) = -1, u(0, x) = 0

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