Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2005 / Paper 1 / 9 / a

Use separation of variables on intervals avoiding zeros of $\cos x$:Taking the tangent gives the real general solutionEach solution is restricted to an interval where both the original equation and this expression are finite. There is no real constant solution because $1+y^2$ never vanishes for real $y$.