The solution of the differential equation $x \frac{dy}{dx} - y = 3$ represents a family of

If $y=y(x)$ is the solution of the differential equation $\left(\frac{2+\sin x}{y+1}\right) \frac{d y}{d x}+\cos x=0$ with $y(0)=1$, then $y\left(\frac{\pi}{2}\right)$ is equal to

Find a particular solution of the differential equation $(x+1) \frac{dy}{dx} = 2e^{-y} - 1$,given that $y = 0$ when $x = 0$.

The equation of the curve passing through the point $(1,0)$ and whose slope is $\frac{y - 1}{x^2 + x}$ is

The general solution of the differential equation $(2x-y)^2 dy - 2(2x-y)^2 dx - 2 dx = 0$ is

Find the particular solution of the differential equation $\log \left(\frac{d y}{d x}\right)=3 x+4 y$ given that $y=0$ when $x=0$.