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  1. MHB Journeyman

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    #1
    When dealing with this separable equation for example, if I'm told to solve the given D.E.

    $y' = x^2/y$

    so after manipulation and taking the integral I got $\frac{y^2}{2} = \frac{x^3}{3} + C$ This is the implicit form correct?

    Would the explicit form be $y = \sqrt{\frac{2}{3} x^3 + C}$

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    #2
    Quote Originally Posted by shamieh View Post
    When dealing with this separable equation for example, if I'm told to solve the given D.E.

    $y' = x^2/y$

    so after manipulation and taking the integral I got $\frac{y^2}{2} = \frac{x^3}{3} + C$ This is the implicit form correct?
    Correct.

    Quote Originally Posted by shamieh View Post
    Would the explicit form be $y = \sqrt{\frac{2}{3} x^3 + C}$
    I would write:

    $y = \pm\sqrt{\frac{2}{3}x^3+C}$

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