If $y=y(x)$ satisfies $\left(\frac{2+\sin x}{1+y}\right) \frac{dy}{dx} = -\cos x$ such that $y(0)=2$,then $y\left(\frac{\pi}{2}\right)$ is equal to

The general solution of the differential equation $\frac{d y}{d x}+\frac{y^2+y+1}{x^2+x+1}=0$ is

The general solution of the differential equation $\cos x \sin y \, dx + \sin x \cos y \, dy = 0$ is

If $y = f(x)$ is a monotonically increasing function such that $(\frac{dy}{dx})^2 = 6 - \frac{dy}{dx}$ and $y(0) = 5$, then $y(3) = ...$

The solution of the differential equation $(2x - 4y + 3) \frac{dy}{dx} + (x - 2y + 1) = 0$ is ($C$ is an arbitrary constant).

The solution curve of the differential equation $2 y \frac{dy}{dx} + 3 = 5 \frac{dy}{dx}$,passing through the point $(0, 1)$,is a conic whose vertex lies on the line: