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I am solving the wave equation with initial position and velocity function:

Remove[y]
equetions = 
  {D[y[x, t], {t, 2}] == (c^2)*D[y[x, t], {x, 2}], 
   y[x, 0] == Sin[x], Derivative[0, 1][y][x, 0] == Sin[x]}
NDSolve[equetions, {t, 0, 100}, {x, -100, 100}]

I am getting the following message:

NDSolve::underdet: There are more dependent variables, {y[x,0],y[x,t],(y^(0,1))[x,0],(y^(0,2))[x,t]}, than equations, so the system is underdetermined. >>

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  • 3
    $\begingroup$ Don't you need to specify boundary conditions as well? $\endgroup$ – march Aug 18 '15 at 1:06
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You cannot have a variable c in your equations that doesn't has a value when you use NDSolve. The function NDSolve is a numerical solver and all parameters need to be specified.

Furthermore, you are missing some boundary conditions for your problem. They are needed to be specified accordingly. Here is a working example of your problem:

eq = {
   D[y[x, t], {t, 2}] == (c^2)*D[y[x, t], {x, 2}],
   y[x, 0] == Sin[x],
   Derivative[0, 1][y][x, 0] == Sin[x],
   y[-Pi, t] == y[Pi, t]
   } /. c -> 1.2

NDSolve[eq, y, {t, 0, 10}, {x, -Pi, Pi}]

Mathematica graphics

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  • $\begingroup$ why do you need y[-Pi, t] == y[Pi, t] isn't initial position and velocity determines everything ? $\endgroup$ – user47376 Aug 18 '15 at 9:48

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