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Help me please to understand how to solve many EDP with Mathematica.

weqn = D[u[x, t], {t, 2}] == D[u[x, t], {x, 2}]
Ivi = {u[x, 0] == 1}
Ibc = {u[0, t] == 0}
Sol = DSolveValue[{weqn, Ivi, Ibc}, u[x, t], {x, t}]
DSolveValue[{(u^(0,2))[x, t] == (u^(2,0))[x, t], {u[x, 0] == 1},{u[0, t] == 0}}, u[x, t], {x, t}]
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1 Answer 1

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Maybe by this way.

sol = DSolve[{Derivative[0, 2][u][x, t] == Derivative[2, 0][u][x, t]},
   u[x, t], {x, t}]
Reduce[(u[x, t] /. First@sol /. t -> 0) == 
   1 && (u[x, t] /. First@sol /. x -> 0) == 0]

{{u[x, t] -> C[1][t - x] + C[2][t + x]}}

C[1][-x] == 1 - C[2][x] && C[1][t] == -C[2][t]

Here C[1], C[2] are two arbitrary(smooth)functions which satisfies the last condition.

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