The general solution of the differential equation $\frac{x dy - y dx}{y} = 0$ is . . . . . . .

Let a curve $y=f(x)$ pass through the points $(0,5)$ and $(\log_e 2, k)$. If the curve satisfies the differential equation $2(3+y) e^{2x} dx - (7+e^{2x}) dy = 0$,then $k$ is equal to

Find the general solution of the differential equation: $y \log y \, dx - x \, dy = 0$.

The solution of the differential equation $x(e^{2y} - 1)dy + (x^2 - 1)e^y dx = 0$ is

If $y=y(x)$ and $\left(\frac{2+\sin x}{y+1}\right) \frac{dy}{dx} = -\cos x$,$y(0)=1$,then $y\left(\frac{\pi}{2}\right) = $

Find a particular solution satisfying the given condition:
$x(x^{2}-1) \frac{dy}{dx}=1; y=0$ when $x=2$