The differential equation $\left( \frac{d^2y}{dx^2} \right)^2 - \left( \frac{dy}{dx} \right)^{1/2} = y^3$ has the degree

Statement $1$: The degrees of the differential equations $\frac{dy}{dx} + y^2 = x$ and $\frac{d^2y}{dx^2} + y = \sin x$ are equal.
Statement $2$: The degree of a differential equation,when it is a polynomial equation in derivatives,is the highest positive integral power of the highest order derivative involved in the differential equation; otherwise,the degree is not defined.

The order and degree of the differential equation $\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^{1/3} + x^{1/4} = 0$ are respectively:

For the differential equation $\frac{d^3 y}{d x^3}=0$,$y=a x^2+b x+c$ is

The number of arbitrary constants in the particular solution of a fourth-order differential equation is . . . . . . .

The differential equation $\frac{d^2y}{dx^2} + x\frac{dy}{dx} + \sin y + x^2 = 0$ is of the following type: