Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Discrete mathematics, continuous mathematics, and probability / 4 / b / iii / Solution

Here the integrating factor is $e^{2\sin x}$, since its logarithmic derivative is $2\cos x$. Multiplying the differential equation by it cancels the right-hand exponential and yields $(e^{2\sin x}y{)}^{\prime }=1$. HenceThis formula is actually defined for every real $x$.