Find the order and degree of the differential equation $\left[1+\left(\frac{dy}{dx}\right)^{2}+\sin \left(\frac{dy}{dx}\right)\right]^{\frac{3}{4}}=\frac{d^{2}y}{dx^{2}}$.

The order and degree of the differential equation $\frac{d^{2} y}{d x^{2}}=\sqrt[3]{1-\left(\frac{d y}{d x}\right)^{4}}$ are respectively

The differential equation representing the family of curves ${y^2} = 2c(x + \sqrt{c}),$ where $c$ is a positive parameter,is of

Consider the following differential equations.
$D_1: y=4 \frac{dy}{dx}+3x \frac{dx}{dy}$
$D_2: \frac{d^2y}{dx^2}=\left(3+\left(\frac{dy}{dx}\right)^2\right)^{\frac{4}{3}}$
$D_3: \left[1+\left(\frac{dy}{dx}\right)\right]^2=\left(\frac{dy}{dx}\right)^2$
The ratio of the sum of the orders of $D_1, D_2$ and $D_3$ to the sum of their degrees is

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

The family of curves $y = Ax + A^3$ is represented by a differential equation of degree: