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Very hard integral

  1. Mar 23, 2006 #1
    g(x) is a function of x that we do not know its form.


    y(t) =(1/2) integral 0-->t [ sin(2t-2x)*g(x) ]dx

    i tried to use integration by substitution and by parts
    but the problem is that g(x) has an unknown form.

    the actual problem is that

    y" +cy' +dy = g(t) y(0) = y0 y'(0) = y'0

    we are asked to find c,d,y0,y'0
    knowing that y(t) is the solution of the second order differential equation.

    i would appreciate your help.
    Thanks,
    Joe
     
  2. jcsd
  3. Mar 24, 2006 #2

    arildno

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    Evaluate y(0) to find y0.

    Differentiate y and evaluate y'(0) to find y'0

    Insert y' and y'' in your equation, and determine c and d from that.

    Remember Leibniz' rule for differentiating an integral with variable limits!
     
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