Solution
= Solution
For $y\ne0$, the <separable differential equation> gives $dy/y^2=dx$. Integrating gives $-1/y=x+C_0$, or
$$
\boxed{y(x)=\frac1{C-x},\qquad x\ne C.}
$$
Each solution is considered on an interval not containing its pole. The additional <stationary solution> $y=0$ is excluded by the stated condition.