The sum of the order and degree of the differential equation $x\left(\frac{d^2 y}{d x^2}\right)^{\frac{1}{2}}=\left(1+\frac{d y}{d x}\right)^{\frac{4}{3}}$ 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 $\frac{d^3y}{dx^3} + \cos(\frac{d^2y}{dx^2}) = 0$, which of the following is true?

If $m$ and $n$ are the order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \right)} + \frac{d^3y}{dx^3} = x^2 - 1$,then

The order of the differential equation $2 x^{2} \frac{d^{2} y}{d x^{2}}-3 \frac{d y}{d x}+y=0$ is

If $m$ is the order and $n$ is the degree of the differential equation $y = \frac{dp}{dx} + \sqrt{a^2 p^2 - b^2}$,where $p = \frac{dy}{dx}$,then the value of $m+n$ is