The solution of the equation $\frac{dy}{dx} = y(e^x + 1)$ is

$A$ 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 solution of the differential equation $(1+x) y \,dx + (1-y) x \,dy = 0$ is

Let $y=y(x)$ be a solution of the differential equation,$\sqrt{1-x^{2}} \frac{dy}{dx}+\sqrt{1-y^{2}}=0, |x| < 1$. If $y\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2}$,then $y\left(\frac{-1}{\sqrt{2}}\right)$ is equal to

The solution of $\frac{dy}{dx} = \frac{x \log(x^2) + x}{\sin y + y \cos y}$ is:

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