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Math Help - Differential Questions

  1. #1
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    Differential Questions

    Solve:

    \frac{dy}{dx}= \frac{y^3}{1-2xy^2},\ \  y(0)=1


    No idea how to do this, tried various methods and came up with nothing. Any Suggestions on how to attempt this one?
    Last edited by CaptainBlack; October 22nd 2009 at 04:52 AM.
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  2. #2
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    Quote Originally Posted by electricalphysics View Post
    Solve:

    \frac{dy}{dx}= \frac{y^3}{1-2xy^2},\ \ y(0)=1


    No idea how to do this, tried various methods and came up with nothing. Any Suggestions on how to attempt this one?
    If you re-write your ODE as

     <br />
\frac{dx}{dy} = \frac{1-2xy^2}{y^3}<br />

    or

     <br />
\frac{dx}{dy} + \frac{2x}{y} = \frac{1}{y^3}<br />

    it's linear in x.
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  3. #3
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    or divide top and bottom by y^3 and put y=tx to turn your equation into a separable one.
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  4. #4
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    Quote Originally Posted by Danny View Post
    If you re-write your ODE as

     <br />
\frac{dx}{dy} = \frac{1-2xy^2}{y^3}<br />

    or

     <br />
\frac{dx}{dy} + \frac{2x}{y} = \frac{1}{y^3}<br />

    it's linear in x.
    Thanks i got it, but
    When am I to know I must flip the dy/dx to make x(y)? Is it because of the particular form of the ODE ?
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  5. #5
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    Quote Originally Posted by electricalphysics View Post
    Thanks i got it, but
    When am I to know I must flip the dy/dx to make x(y)? Is it because of the particular form of the ODE ?
    When it works! Many mathematics problems are solved by "try this and if it doesn't work try that". The important thing is to try.
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