Let y = y(x) be the solution of the differential equation $\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0$. Then, $y\left( {{\pi \over 3}} \right)$ is equal to :

Question

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

$\cos x(3\sin x + \cos x + 3)dy = (1 + y\sin x(3\sin x + \cos x + 3))dx,0 \le x \le {\pi \over 2},y(0) = 0$. Then, $y\left( {{\pi \over 3}} \right)$ is equal to :

$2{\log _e}\left( {{{\sqrt 3 + 7} \over 2}} \right)$

$2{\log _e}\left( {{{3\sqrt 3 - 8} \over 4}} \right)$

$2{\log _e}\left( {{{2\sqrt 3 + 10} \over {11}}} \right)$

$2{\log _e}\left( {{{2\sqrt 3 + 9} \over 6}} \right)$

Solution

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