The order of the differential equation $\frac{d^2 y}{d x^2}=\sqrt{1-\left(\frac{d y}{d x}\right)^2}$ is

The order and degree of the differential equation $\sqrt[3]{\frac{d^2 y}{d x^2}}=\sqrt{\frac{d^3 y}{d x^3}}$ are . . . . . . and . . . . . . .

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 order and the degree of the differential equation $\sqrt{1 + (\frac{d^2y}{dx^2})^2} = \sqrt[3]{x + (\frac{dy}{dx})^3}$ are respectively . . . . . . and . . . . . . .

Determine the order and degree (if defined) of the differential equation $y^{\prime} + y = e^{x}$.

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