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Wave eqn with initial functions odd

  1. Oct 3, 2004 #1
    If both u(x,0)=φ(x) and Ut(x,0)=ψ(x) are odd functions of x, then the solution to wave equation u(x,t) is odd for all t.

    odd means f(x)=- f(-x)

    the general solution is
    u(x,t)=(1/2)*[φ(x+ct)+φ(x-ct)]+(1/2c)*(integral ψ(s)ds, from x-ct to x+ct)

    can anyone help?
    Last edited: Oct 3, 2004
  2. jcsd
  3. Oct 4, 2004 #2
    if i understand correct, you need to prove that U(x,t)=-U(-x,t)
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