Past exam of the algebra 1 and differential equations 1 course of the University of Oxford / 2014 / 4 / b / i / Solution

Dividing by $x^2$, which is allowed precisely away from zero, givesThis function is smooth on each of the two half-planes $x>0$ and $x<0$, and is affine in the dependent variable $y$. Its derivative with respect to $y$ is $(1-2x)/x^2$.