JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 77

The integrating factor is $\sec x$: $(y\sec x)'=2\sin x$, so $y\sec x=-2\cos x+c$. $y(0)=1$ gives $c=3$.

At $x=\pi$: $-y=2+3$, so $y(\pi)=-5$.