The solution of the differential equation $e^x y dx + e^x dy + x dx = 0$ is

The equation of the curve passing through the point $(1, 1)$ such that the slope of the tangent at any point $(x, y)$ is equal to the product of its coordinates is

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

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

If $y=y(x), y \in [0, \frac{\pi}{2})$ is the solution of the differential equation $\sec y \frac{dy}{dx} - \sin(x+y) - \sin(x-y) = 0$,with $y(0)=0$,then $5y'(\frac{\pi}{2})$ is equal to $......$

Find the general solution of the differential equation: $\frac{dy}{dx} = \sqrt{4 - y^2}$ where $-2 < y < 2$.