If $\frac{dy}{dx} + \frac{1}{\sqrt{1 - x^2}} = 0$,then

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

The general solution of the differential equation $y y^{\prime} = x \left[ \frac{y^2}{x^2} + \frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)} \right]$,where $\phi$ is an arbitrary function,is

The general solution of the differential equation $\sec^{2} x \tan y \, dx + \sec^{2} y \tan x \, dy = 0$ is

If $\frac{dy}{dx} = y + 3$ and $y(0) = 2$,then find the value of $y(\log 2)$.

The equation of a curve passing through the point $(0,1)$,given that the slope of the tangent to the curve at any point $(x, y)$ is equal to the sum of the $x$-coordinate and the product of $x$ and $y$ coordinates at that point,is