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\(\begin{equation} \begin{aligned} &f(y) \text { is the solution of differential equation }\\ &\left(1+y^2\right…

Q1

\(\begin{equation}
\begin{aligned}
&f(y) \text { is the solution of differential equation }\\
&\left(1+y^2\right)+\left(x-2 \tan ^{-1} y\right) \frac{d y}{d x}=0, f(0)=1, \text { find } f\left(\frac{1}{\sqrt{3}}\right) .
\end{aligned}
\end{equation}\) (22 Jan, Shift II, Memory Based)

a

\(\frac{\pi }{3}-2+3{e}^{-\pi /6}\)

b

\(\frac{\pi }{6}-2+3{e}^{-\pi /6}\)

c

\(\frac{\pi }{3}-2+3{e}^{-\pi /3}\)

d

None of these

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