question_answer

If y(x) satisfies the differential equation \[y'y\,\tan x=2\,\,\sec x\] and \[y(0)=0,\] then which one among the following is true?

A)  \[y'\,\,\left( \frac{\pi }{4} \right)=\frac{{{\pi }^{2}}}{6\sqrt{2}}\]

B)  \[y'\,\,\left( \frac{\pi }{4} \right)=\frac{\pi }{\sqrt{2}}+\frac{{{\pi }^{2}}}{3\sqrt{2}}\]

C)  \[y'\,\,\left( \frac{\pi }{3} \right)=\frac{4\pi }{3}+\frac{2{{\pi }^{2}}}{3\sqrt{3}}\]

D)  All the above

E)  None of these