The solution of the differential equation $\frac{dy}{dx} + \sin^2 y = 0$ is

The solution of the differential equation $({e^x} + 1)y \, dy = (y + 1){e^x} \, dx$ is:

The solution of $y' = 1 + x + y^2 + xy^2$,$y(0) = 0$ is

The solution of $\frac{dy}{dx} = \left( \frac{y}{x} \right)^{1/3}$ is

If a curve passes through the point $\left( 2, \frac{7}{2} \right)$ and has slope $\left( 1 - \frac{1}{x^2} \right)$ at any point $(x, y)$ on it,then the ordinate of the point on the curve whose abscissa is $-2$ is

If $y=y(x), y \in [0, \frac{\pi}{2})$ is the solution of the differential equation $\sec y \frac{dy}{dx} - \sin(x+y) - \sin(x-y) = 0$,with $y(0)=0$,then $5y'(\frac{\pi}{2})$ is equal to $......$