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Math Help - Exact Differential Equation

  1. #1
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    Exact Differential Equation

    need your help on this...



    2xy dx + (y^2 - x^2) dy = 0

    Answer: x^2 + y^2 = cy
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  2. #2
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    It's also homogeneous, or you do need to solve it as a exact one?
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  3. #3
    Super Member Random Variable's Avatar
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    That's not an exact equation unless it's  -2xydx +(y^{2}-x^{2}) dy =0 or  2xydx +(y^{2}+x^{2}) dy =0
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  4. #4
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    thanks.
    you're right, it's homogeneous.

    a little need help please.

    i'm stuck in the ending part.

    ln |y| + ln |v^2 + 1| = c
    how come that c has a y ( cy )

    thanks.
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  5. #5
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    Quote Originally Posted by redfox2600 View Post

    i'm stuck in the ending part.

    ln |y| + ln |v^2 + 1| = c
    how come that c has a y ( cy )
    Suppose that you actually got \ln y+\ln(v^2+1)=k, then put k=\ln c ('cause both of them are constants), thus your equation becomes y\big(v^2+1\big)=c, because of injectivity.
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  6. #6
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    thanks for big help Krizalid.
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  7. #7
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    the ODE is not exact, so you should find an "intergrating factor" to multiply with the original ODE so that the NEW ODE is solvable. R u interested on how to solve the problem?
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  8. #8
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    yes. thanks for the great help.
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