Integrating factor of $(x+2 y^3) \frac{d y}{d x}=y^2$ is

If $y=y(x)$ is the solution curve of the differential equation $\frac{dy}{dx} + y \tan x = x \sec x$,$0 \leq x \leq \frac{\pi}{3}$,with $y(0)=1$,then $y\left(\frac{\pi}{6}\right)$ is equal to

Which one of the following is a linear differential equation?

If $y=y(x)$ is the solution of the differential equation $x \frac{d y}{d x}+2 y=x e^{x}, y(1)=0$,then the local maximum value of the function $z(x)=x^{2} y(x)-e^{x}$,$x \in R$ is

The solution of $\cos y + (x \sin y - 1) \frac{dy}{dx} = 0$ is

The solution of the equation $(x-4y^3) \frac{dy}{dx}-y=0, (y>0)$ is