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Linear equations - use of integrating factor

  1. Nov 24, 2012 #1
    Hi, I am doing self study and have hit a snag in the road. Can someone please clarfiy this for me. I am reading K.A. Stroud's Engineering Mathematics which so far has been great.


    Consider the equation [itex]\frac{dy}{dx}[/itex] + 5y = e2x

    In this case, we begin multiplying both sides by e5x. This gives

    e5x[itex]\frac{dy}{dx}[/itex] + y5e5x = e2x.e5x = e7x

    We now find that the left-hand-side is the derivative of y.e5x.

    [itex]\frac{d}{dx}[/itex](y.e5x) = e7x


    ____________________

    Can someone please clarify how the left hand side is the derivative of y.e5x.

    I get that y5e5x is the derivative of y.e5x, but what about the first part of the left-hand-side. What happens to the e5x[itex]\frac{dy}{dx}[/itex]
     
  2. jcsd
  3. Nov 24, 2012 #2

    lurflurf

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    Homework Helper

    The product rule is

    (uv)'=u'v+uv'

    here u=y v=e^(5x)

    You have taken y'=0
     
  4. Nov 24, 2012 #3
    Thanks alot lurflurf. It seems so obvious now!

    I was treating y as a constant. doh
     
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