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Let \(y=y(x)\) be in the solution of the differential equation \(\cos x(3\sin x+\cos x+3)dy=(1+y\sin x(3\sin x+\cos x+3)…

Q1

Let \(y=y(x)\) be in the solution of the differential equation \(\cos x(3\sin x+\cos x+3)dy=(1+y\sin x(3\sin x+\cos x+3))dx,0\leq x\leq \frac{\pi }{2},y(0)=0\).

Then \(y\left(\frac{\pi }{3}\right)\) is equal to:

[JEE Main 2021, 17 Mar (Shift 2)]

a

\(2{\log }_{e}\left(\frac{2\sqrt{3}+10}{11}\right)\)

b

\(2{\log }_{e}\left(\frac{2\sqrt{3}+9}{6}\right)\)

c

\(2{\log }_{e}\left(\frac{\sqrt{3}+7}{2}\right)\)

d

\(2{\log }_{e}\left(\frac{3\sqrt{3}-8}{4}\right)\)

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