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

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.

The initial condition gives $1=1/(C-1)$, hence $C=2$. ThusThe displayed interval is the maximal connected interval containing the initial point $x=1$; the solution of a differential equation diverges at $x=2$.