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1D wave equation

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November 7th, 2022

Solve the following string equation problem


utt = 1/4* uxx, 0<x<1,t>0,
u(0, t) = 0, u(1,t)=0, t>0

1/2 * x, 0< x<1/2
u(x,0) =
1−x, 1/2<x<1.

ut (x,0) = 0

Solve using separation of variables and D’Alembert. Show solutions in detail.
Graph both solution u(x, t) for t = 0, 1, 2, 4.

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