The order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt{1-\left(\frac{d y}{d x}\right)^2}$ is

Determine the order and degree (if defined) of the differential equation $y''' + 2y'' + y' = 0$.

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

The degree of the differential equation $\left( \frac{d^3y}{dx^3} \right)^{\frac{2}{3}} + 4 - 3\frac{d^2y}{dx^2} + 5\frac{dy}{dx} = 0$ is

The degree and order of the differential equation of the family of parabolas whose axis is the $X$-axis, are respectively

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ is . . . . . . .