Degree of the differential equation $e^{\frac{dy}{dx}} + (\frac{dy}{dx})^3 = x$ is

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

The degree and order of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^3\right]^{\frac{7}{3}}=7\left(\frac{d^2y}{dx^2}\right)$ respectively are

$p$ 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:

For the differential equation $\left[1-\left(\frac{dy}{dx}\right)^2\right]^{5/2} = 8 \frac{d^2y}{dx^2}$,the order and degree are:

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