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

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

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

If the order and degree of the differential equation $\left(\frac{d^2 y}{dx^2}\right)^5 + 4 \frac{\left(\frac{d^2 y}{dx^2}\right)^5}{\left(\frac{d^3 y}{dx^3}\right)} + \frac{d^3 y}{dx^3} = \sin x$ are $m$ and $n$ respectively,then the value of $(m^2 + n^2)$ is equal to

If $c_1, c_2, c_3, c_4, c_5$ are arbitrary constants,then the order of the differential equation whose general solution is $y=(c_1+c_2) \sin (x+c_3)+c_4 e^{x+c_5}$ is