1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

    The product rule is


    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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook