The solution of the differential equation $\begin{align*} \frac{dy}{dx} + \frac{y}{2} \sec x = \frac{\tan}{2\;y}, \end{align*}$ where $0 \leq x < \frac{\pi}{2},$ and $y(0)= 1,$ is given by

Question

$\begin{array}{1 1}(1)\; y = 1 - \frac{x}{\sec x + \tan x} \\ (2) \; y^2 = 1 + \frac{x}{\sec x + \tan x} \\ (3)\; y^2 = 1 - \frac{x}{\sec x + \tan x} \\ (4)\; y = 1 + \frac{x}{\sec x + \tan x} \end{array} $