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

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

Let $y=y(x)$ be the solution of the differential equation $e^{x} \sqrt{1-y^{2}} dx + \frac{y}{x} dy = 0$,with $y(1) = -1$. Then the value of $(y(3))^{2}$ is equal to:

If the solution $y(x)$ of the given differential equation $(e^y+1) \cos x \, dx + e^y \sin x \, dy = 0$ passes through the point $(\frac{\pi}{2}, 0)$,then the value of $e^{y(\frac{\pi}{6})}$ is equal to ...........

If $2x - y + c \log(x - 2y - 4) = k$ is the general solution of $\frac{dy}{dx} = \frac{2x - 4y - 5}{x - 2y + 2}$,then $c =$

The solution of the differential equation $\frac{dy}{dx} = \frac{xy+y}{xy+x}$ is