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Student Support Forum: 'wave equation' topicStudent Support Forum > General > "wave equation"

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VR
04/18/13 09:05am

Equation without boundary and initial conditions

DSolve[D[c^2*u[x, t], {x, 2}]
- D[u[x, t], {t, 2}] == 0, u[x, t], {x, t}]

gives well known solution

C[1][t - x/Sqrt[c^2]] + C[2][t + x/Sqrt[c^2]]

However, if I add these conditions

DSolve[{D[c^2*u[x, t], {x, 2}]
- D[u[x, t], {t, 2}] == 0,
u[x, 0] == Sin[Pi*x/L],
{D[u[x, t], t] /. t -> 0} == 0,
u[0, t] == 0, u[L, t] == 0}, u[x, t], {x, t}]

there is no solution, DSolve is just repeated without any error messages.

Where is mistake?


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