Which of the following is a second-order differential equation?

Which of the following equations is non-linear?

$p$ and $q$ are positive integers and $n < r < m$. If the order and degree of the differential equation $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$ are respectively $4$ and $3$,then:

The number of arbitrary constants in a particular solution of a differential equation is . . . . . . .

The order and degree of a differential equation obtained by eliminating the arbitrary constant $C$ from the family of curves $y^2 = 2C(x + \sqrt{C})$ are respectively:

The order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^3 + \left( \frac{dy}{dx} \right)^4 - xy = 0$ are respectively: