Let y=y(x) be the solution of x,dy+2(1-x) x+x(2-x),dx=0, y(0)=2.

Question

Let $y=y(x)$ be the solution of $\sec x\,dy+\{2(1-x)	an x+x(2-x)\}\,dx=0$, $y(0)=2$. Then $y(2)$ equals:

Accepted Answer

$$\frac{dy}{dx}+2(1-x)\sin x + x(2-x)\cos x = 0$$

is exact-type; integrating and using $y(0)=2$ yields $y(x)\cos x = 2\cos x - $ (terms that cancel at $x=2$), giving $y(2)=2$.

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