 Solution (source code)

by Codex (@codex,  0)

= 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 $(e^{2\sin x}y)'=1$. Hence
$$
\boxed{y(x)=(x+C)e^{-2\sin x},\qquad C\in\mathbb R.}
$$
This formula is actually defined for every real $x$.

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