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How to reduce?

  1. Aug 23, 2005 #1
    How to reduce the equation: Show how the equation u(t)+Int( 0->t) {[e^a(t-t1)]u(t1)}dt1 = k can be reduced to a differential equation and obtain an intial condidtion for the equation.

    Remarks: Int(0->t): integral from 0 to t !
  2. jcsd
  3. Aug 23, 2005 #2


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    Evaluate your equation at t=0. What does that say about u(0)?

    Differentiate your equation to get your differential equation.
  4. Aug 23, 2005 #3
    Yes I know I have to differential but if the diff. it with respect to t , what will happen to the second term on the left hand side?
  5. Aug 23, 2005 #4


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    Use the Leibniz Integral Rule.
    \frac{\partial}{\partial t}f(x,t)dx+f(x,t){\partial x}{\partial t}\right|_{x=a(t)}^{x=b(t)}[/tex]
    for the initial condition you should know that
    [tex]\int_0^0 f(x) dx=0[/tex]
    Last edited: Aug 23, 2005
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