I want to find constant solutions of the differential equation $\frac{dy}{dx}=\frac{y^3}{x^2}-2\frac{y}{x}$. I set $y=c$, where $c$ is a constant. Then $\frac{dy}{dx}=0$ and the differential equation becomes

$0=\frac{c^3}{x^2}-2\frac{c}{x}$

$\frac{c}{x}(\frac{c^2}{x}-2)=0$

$c/x=0$ or $c^2/x-2=0$

$c=0$ or $c^2=2x$

How to explain in words the equation $c^2=2x$ does not give any constant solution of the differential equation?