The solution of the differential equation $x \, dy + y \, dx - \sqrt{1 - x^2 y^2} \, dx = 0$ is

Find the general solution of the differential equation: $e^{x} \tan y \, dx + (1 - e^{x}) \sec^{2} y \, dy = 0$.

The equation of the curve whose slope at any point is equal to $2xy$ and which passes through the point $(0,1)$ is

Let a smooth curve $y=f(x)$ be such that the slope of the tangent at any point $(x, y)$ on it is directly proportional to $\left(\frac{-y}{x}\right)$. If the curve passes through the points $(1, 2)$ and $(8, 1)$,then $\left| y \left(\frac{1}{8}\right) \right|$ is equal to

The general solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ is given by

$A$ curve passing through $(2, 3)$ and satisfying the differential equation $\int\limits_0^x {t\,y(t)\,dt} = x^2y(x)$ for $x > 0$ is