Integral Function Differential Equation (Jee Ma…

First Order Differential Equations

Medium

Integral Function Differential Equation

Let g be a differentiable function such that $\int\limits_0^x {g\left( t \right)dt} = x - \int\limits_0^x {tg\left( t \right)dt}$ , x ≥ 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

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