The general solution of the differential equation $x\,dx = (x^2+1)\,dy$ is (where C is an arbitrary constant)

Which one of the following equations is a homogeneous differential equation?

Let $e^{\alpha y} + e^{\beta y} + \gamma x^2 + \delta \log|x| + C = 0$, where $C \in \mathbb{R}$ be a particular solution of the differential equation $x(e^{2y} - 1)dy + (x^2 - 1)e^ydx = 0$ and passes through the point $(1, 1)$. The value of $(\alpha + \beta + \gamma + \delta - C)$ is

The particular solution of the differential equation $\sec^2x\tan y\,dx - \sec^2y\tan x\,dy = 0$, $y=\frac{\pi}{4}$ when $x=\frac{\pi}{4}$, is

The general solution of the differential equation $(x^2 - yx^2)dy + (y^2 + x^2y^2)dx = 0$ is:

The particular solution of the differential equation $\frac{dy}{dx} + \frac{3y}{x} = 0$, $y(1) = 1$ is

The solution of the differential equation $\dfrac{dy}{dx} = \dfrac{x+2}{3-y}, (y \neq 3), y(0) = 0$

represents