If y=y(x) is the solution curve of dydx+y x = x x, 0 x3, y(0)=1, then y(6) is:

Question

If $y=y(x)$ is the solution curve of $\dfrac{dy}{dx}+y	an x = x\sec x$, $0\le x\le\dfrac{\pi}{3}$, $y(0)=1$, then $y\left(\dfrac{\pi}{6}ight)$ is:

Accepted Answer

I.F. $=\sec x$. $y\sec x = x	an x-\ln(\sec x)+c$. Using $y(0)=1 \Rightarrow c=1$.

At $x=\pi/6$: $y = \dfrac{\pi}{12}+\dfrac{\sqrt3}{2}\ln\left(\dfrac{\sqrt3}{2}ight)+\dfrac{\sqrt3}{2}$, which simplifies to option A.

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