The order and degree of the differential equation $\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^{1/3} + x^{1/4} = 0$ are respectively:

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

The degree of the differential equation $y(x) = 1 + \frac{dy}{dx} + \frac{1}{2!} \left( \frac{dy}{dx} \right)^2 + \frac{1}{3!} \left( \frac{dy}{dx} \right)^3 + \dots$ is

The degree of the given differential equation $\left( \frac{d^2y}{dx^2} \right)^3 = \left( 1 + \frac{dy}{dx} \right)^{1/2}$ is:

$p$ and $q$ are positive integers and $n < r < m$. If the order and degree of the differential equation $\left(\frac{d^m y}{d x^m} + \frac{d^n y}{d x^n}\right)^{p/q} = 5 \frac{d^r y}{d x^r}$ are respectively $4$ and $3$,then:

The order and degree of the differential equation $\sqrt{\frac{dy}{dx}} - 4\frac{dy}{dx} - 7x = 0$ are respectively: