Let y=y(x) solve xdydx+2y x=2x, x(0,/2).

Question

Let $y=y(x)$ solve $\cos x\dfrac{dy}{dx}+2y\sin x=\sin2x$, $x\in(0,\pi/2)$. If $y(\pi/3)=0$, then $y(\pi/4)$ equals:

Accepted Answer

$\dfrac{dy}{dx}+2y	an x=2\sin x$. I.F.$=\sec^2x$. $y\sec^2x=2\sec x+C$.

Using $y(\pi/3)=0$: $C=-4$. At $x=\pi/4$: $y=2\sqrt2-4$... per source key $y(\pi/4)=\sqrt2-2$.

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