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Let \(y=y(x)\) be 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 the solution of the differential equation

\(\cos x(3 \sin x+\cos x+3) dy=(1+y \sin x(3 \sin x+\cos x+3))\) \(d x, 0 \leq x \leq \frac{\pi}{2}, y(0)=0\).

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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