The solution of the differential equation $2 x \left(\frac{d y}{d x}\right) - y = 4$ represents a family of

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

$A$ curve having the condition that the slope of the tangent at any point $(x, y)$ is two times the slope of the straight line joining the same point to the origin $(0, 0)$ is a/an:

Solve $xdx + ydy = \frac{xdy - ydx}{x^2 + y^2}$

$A$ particle moves in a straight line with a velocity given by $\frac{dx}{dt} = x + 1$ (where $x$ is the distance covered). The time taken by the particle to traverse a distance of $99 \ m$ is:

The particular solution of $\frac{dy}{dx} = 1 + x + y^2 + xy^2$,when $y(0) = 0$,is