= Solution
On an <interval> with $x\ne0$, the equation is a <separable differential equation>. For $y\ne0$,
$$
\frac{dy}{y^2}=\left(\frac4{x^2}-x^2\right)dx.
$$
Taking <antiderivatives> gives $-1/y=-4/x-x^3/3+C$. Renaming the constant, the explicit general nonzero solution is
$$
\boxed{y(x)=\frac1{4/x+x^3/3+C}.}
$$
It is defined on any <interval> avoiding $x=0$ and zeros of its denominator. The separation divided by $y^2$, so the additional solution $\boxed{y(x)\equiv0}$ must be included.
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