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Differential equations question

  1. Oct 28, 2007 #1
    i have this equation:
    dx/dt = t/(x*t^2+x^3)

    using the substitution u = t^2, i obtain the following equation:

    du/dx = 2u/(ux+x^3)

    does anybody know how i can solve this equation?
  2. jcsd
  3. Oct 28, 2007 #2


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    Science Advisor

    No, you don't obtain that equation. If u= t^2, then dx/dt= dx/du du/dt=2t dx/du.
    The equation becomes 2t dx/du= t/(xu+ x^3) or dx/du= 1/(2(xu+x^3). Then
    du/dx= 2(xu+ x^3). Unfortunately, since we still cannot separate u and x, that doesn't really help.
  4. Oct 28, 2007 #3
    ah, my bad,

    okay, this problem is now very easy then since its linear and i can just use an integrating factor
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