Mathematics - Differential Equation Question with Solution | TestHub

Let $g$ be a differentiable function such that ${\int }_0^{x}g(t)dt=x-{\int }_0^x\mathrm{tg}(t)dt,x\ge 0$ and let $y=y(x)$ satisfy the differential equation $\frac{dy}{dx}-y\tan x=$ $2(x+1)\sec xg(x),x\in \left[0,\frac{\pi }{2}\right)$. If $y(0)=0$, then $y\left(\frac{\pi }{3}\right)$ is equal to