Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2017 / Paper 1 / 9 / a

For $y\ne 0$, the separable differential equation gives $dy/y^2=dx$. Integrating gives $-1/y=x+C_0$, orEach solution is considered on an interval not containing its pole. The additional stationary solution $y=0$ is excluded by the stated condition.