The solution of the differential equation $x dy - y dx = 0$ represents:

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

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

General solution of the differential equation $\log \left(\frac{d y}{d x}\right)=a x+b y$ is

The differential equation $\cos (x+y) dy = dx$ has the general solution given by

Let $S$ be the family of curves given by the general solution of the differential equation $\frac{y^2 e^{-1 / y}}{\sqrt{x}} dx - 2 \sec \sqrt{x} dy = 0$. Then the equation of the curve belonging to $S$ and passing through $(\pi^2, 1)$ is