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Convolution and a diff eq

  1. Sep 30, 2006 #1
    Any hints to this problem?

    "Assume the solution to a differential equation is given by
    [tex]\frac{dy(x)}{dx}+ay(x) = f(x)[/tex]
    where [itex]y(0)=y_0[/itex] and a is a constant. Show how y(x) can be written as a convolution of f(x) and an exponential [itex]e^{ax}[/itex]."

    The only hint we got from the prof was to multiply both sides by the exponential and express the left as a single term, but I could be doing something wrong there as well. Anyone have any more hints? (I don't want the solution just yet, I just want to try to work it out first)

  2. jcsd
  3. Oct 1, 2006 #2
    Upon multiplying both sides with the exponential, recall next that
    [tex]\frac{d(uv)}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}[/tex]
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