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How do you solve this differential equation?

  1. Nov 11, 2007 #1

    Simfish

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    http://simfish.googlepages.com/snap000672.jpg

    Okay, so I tried to separate the (1-W/b) term by letting it go into the denominator. But then you can't really solve the equation by the traditional dW/W method, since W + constant is raised to a power of n. i could multiply both sides by (1-W/b) to a power of n-1, but then when i integrate, i don't get the desired answer. can anyone help? thanks
     
  2. jcsd
  3. Nov 12, 2007 #2

    HallsofIvy

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    You have
    [tex]\frac{dW}{dz}= \frac{M}{(1-\frac{z}{a})(1-\frac{W}{b})^n}[/tex] W(0)= 0

    That separates as
    [tex](1- \frac{W}{b})^n dW= \frac{M dz}{(1-\frac{z}{a})}[/tex]
    I'm not sure what you mean by "the traditional dW/W method" but if you mean just integrating to get ln(W), that works in only a tiny fraction of such separable differential equations. To integrate the left side, I would recommend letting u= 1- W/b so that du= -dW/b and the integral becomes
    [tex]\int (1- \frac{W}{b})^n dW= -\frac{1}{b}\int u^n du[/tex]
     
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