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Tough Differential Equation (for me at least, and some others)

  1. Apr 13, 2010 #1

    Char. Limit

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    Gold Member

    So, I tried putting this on the homework forum, but no one could think of a solution. So I'm going to put it here, hoping someone here would know...

    How would you solve this?

    [tex]\frac{dy}{dx}=5x^2-\frac{6}{y-2}[/tex]

    Note: This is no longer homework (it was a challenge question, but the challenge was thrown out; the teacher found it too difficult), so don't worry about spoiling anything.

    Also: So far, (I'm learning diff EQs independently, and the challenge question was for a Calculus class) I only know the methods of substitution and finding an integration factor. I've heard of transforms, though. Could any of them help? Laplace, maybe?
     
  2. jcsd
  3. Apr 13, 2010 #2

    Mute

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    Homework Helper

    That's a non-linear differential equation. Methods like the Laplace transform or methods you learn in an ODE course won't be of much help.

    Wolfram alpha doesn't even give a closed form solution:

    http://www.wolframalpha.com/input/?i=solve+y%27%28x%29+%3D+5*x^2-6%2Fy%28x%29

    (note that dy/dx = d(y-2)/dx, so you can make the substitution y - 2 = z, which I relabelled y)
     
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