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Homework Help: Separation of Variables Help

  1. Oct 2, 2006 #1
    http://album6.snapandshare.com/3936/45466/844588.jpg [Broken]
     
    Last edited by a moderator: May 2, 2017
  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
     
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