MHB Need reassurance on "implicit" and "explicit" form

[shamieh]

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

 

[MarkFL]

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. :D

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

I would write:

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