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:

If $a$ and $b$ are respectively the order and degree of the differential equation $y^2(y^{\prime \prime})^2 + 3x(y^{\prime})^{1/3} + x^2y^2 = \sin x$,then:

For the differential equation given below,determine its order and degree (if defined).
$\frac{d^{4} y}{d x^{4}}-\sin \left(\frac{d^{3} y}{d x^{3}}\right)=0$

Find the sum of the order and degree of the differential equation $y = x(\frac{dy}{dx})^3 + \frac{d^2y}{dx^2}$.

The order of the differential equation,whose general solution is given by $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$,where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constants,is

If $m$ and $n$ are the degree and order of the differential equation $\left(1+y_{1}^{2}\right)^{2 / 3}=y_{2}$,then the value of $\frac{m+n}{m-n}$ is