Hey arcticreaver.
What exactly are you trying to solve?
That's incorrect...in general you want to arrange with the terms having dy/dx as a factor on one side and the other terms on the other. Then factor out dy/dx, and divide through by the other factor to isolate dy/dx. Give this another try...
Just in case a picture helps (and otherwise to correct a small slip/typo, in Mark's differentiation of y^3)...
... where (key in spoiler) ...
Spoiler:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!