The solution of the differential equation $x \, dy - y \, dx = 0$ represents a

The solution of $y' = 1 + x + y^2 + xy^2$,$y(0) = 0$ is

The particular solution of the differential equation $\frac{dy}{dx} = \frac{x+y+1}{x+y-1}$ when $x = \frac{2}{3}$ and $y = \frac{1}{3}$ is

The solution of the differential equation $\sin ^{-1}\left(\frac{dy}{d x}\right)=x+y$ is

The solution of the differential equation $e^{2y} (1 + \ln x)dx + \csc y (2 + \cot y)dy = 0$ satisfying $y(1) = \frac{\pi}{2}$ 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: