Past exam of the mathematical methods I course of the University of Oxford / 2022 / 11 / a / Solution

Separation of variables gives $\ln |y|=\sqrt{1+x^2}+C$ for a nonzero solution. Including the zero solution in the arbitrary real amplitude givesDifferentiating the exponent verifies the equation. This form keeps the zero solution that a division by $y$ could otherwise conceal.