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Math Help - Find in implicit form, the general solution of a differential equation

  1. #1
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    Find in implicit form, the general solution of a differential equation

    I was asked to show that ∫ (1+e^4x)/〖(4x+e^4x)〗^3 dx= -1/(8(4x+e^3x )^2 )+c (x>0)
    And I did.
    But the next question goes "hence find, in implicit form, the general solution of the differential equation dy/dx= -(〖4e〗^(-2y) (1+e^4x ))/(4x+e^4x )^3 (x>0)"

    I am not sure what to do can I get some help please
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  2. #2
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    Re: Find in implicit form, the general solution of a differential equation

    Well, the obvious thing to do is to convert the differential equation to an integral isn't it?
    \frac{dy}{dx}= \frac{4e^{2y}(1+ e^{4x})}{(4x+ e^{4x})^3}
    so \frac{dy}{ye^{2y}}= \frac{(1+ e^{4x})}{(4x+ e^{4x})^3}dx
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  3. #3
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    Re: Find in implicit form, the general solution of a differential equation

    I have tried that but seem to end up in a bit of a mess
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  4. #4
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    Re: Find in implicit form, the general solution of a differential equation

    Actually I think I have it now, Thanks
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