Mathematics Question from JEE Main 2025 · 3 April, Shift 1

Let $g$ be a differentiable function such that $\int_0^x g(t) \, dt = x - \int_0^x t g(t) \, dt$, $x \ge 0$ and let $y = y(x)$ satisfy the differential equation $\frac{dy}{dx} - y \tan x = 2(x+1) \sec x g(x)$, $x \in \left[ 0, \frac{\pi}{2} \right)$. If $y(0) = 0$, then $y\left( \frac{\pi}{3} \right)$ is equal to](streamdown:incomplete-link)