1. Not finding help here? Sign up for a free 30min 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!

Separation of Variables Help

  1. Oct 2, 2006 #1
    [​IMG]
     
  2. jcsd
  3. Oct 2, 2006 #2
    [tex] \frac{dy}{dx} = e^{3x} \times e^{2y} [/tex] So [tex] \int \frac{dy}{e^{2y}} = \int e^{3x} dx [/tex].
     
    Last edited: Oct 2, 2006
  4. Oct 2, 2006 #3
    but the original problem had e raised to the 3x + 2y. The only way I know to get rid of that is to take the natural log of both sides right? If you do that, you are left with ln (dy/dx) on the left side. How did you get rid of the natural log there?
     
    Last edited: Oct 2, 2006
  5. Oct 2, 2006 #4
    By the properties of exponents we know that [tex] e^{3x+2y} = e^{3x}\times e^{2y} [/tex]. So we can separate variables without taking the natural log of both sides. In general, [tex] a^{n+m} = a^{n}\times a^{m} [/tex]
     
  6. Oct 2, 2006 #5
    oOh... :bugeye: I can't believe I didn't see that!! sigh... it is those little things that get me all the time.

    thank you so much for your help
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Separation of Variables Help
Loading...