Differential equation $(y')^3+y^3-yy'=0?$

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How to solve differential equation $$(y')^3+y^3-yy'=0?$$ I tried parametrization $y'=p$, Laplace transformation...

After a while, I have solved it by help of WolframAlpha...

And idea is to divide with $y^3$, and further on it is easy.

But now, I'm interested if this differential equation has origins in statistical physics? Any help or hint is welcome. Thanks in advance.