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Math Help - mixed variable integration coefficient

  1. #1
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    mixed variable integration coefficient

    (y^{4}-4xy)dx+(2xy^{3}-3x^{2})dy=0
    prove that this equation has an xy dependant integration coefficient
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  2. #2
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    show that exist constants that verify \displaystyle\frac{\partial M}{\partial y}-\frac{\partial N}{\partial x}=m\frac{N}{x}-n\frac{M}{y}.
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  3. #3
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    why??
    if the left side equals zero then we have potential and could be solved without multilying by integration coefficient.
    what the right side says ?
    why this equation says about the coefficient
    ?
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  4. #4
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    the condition i gave you gives you the integrating factor, if those constants exist, then the integrating factor is u(x,y)=x^my^n, but on your question you were asked to show that your equation has a integrating factor which depends of xy, so that will force that m=n in order to have u(x,y)=h(xy).
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  5. #5
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    how you got this formula?
    so if u(x,y)=xy then m=n=1
    4y^3-4x-(2y^3-6x)=m\frac{2xy^3-3x^2}{x}-n\frac{y^4-4xy}{y}
    what to do now?
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  6. #6
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    c'mon, simplify, do the algebra.
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  7. #7
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    4y^3-4x-(2y^3-6x)=n(2xy^4-3x^2y-y^4x-4x^2y)
    \frac{4y^3-4x-(2y^3-6x)}{(2xy^4-3x^2y-y^4x-4x^2y)}=n
    i cant get a number out of it
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