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

The order of the differential equation whose solution is $y = a\cos x + b\sin x + c{e^{ - x}}$ is

The number of arbitrary constants that appear in the general solution of the differential equation $\left(\frac{d^4 y}{d x^4}+\frac{d^2 y}{d x^2}\right)^{3 / 2}=5 \frac{d^3 y}{d x^3}$ is

The order and degree of the differential equation $e^{\frac{d^2 y}{d x^2}} = x$ are . . . . . . respectively.

Determine the order and degree (if defined) of the differential equation $y^{\prime \prime} + 2y^{\prime} + \sin(y) = 0$.

The order and degree of the differential equation $\frac{dy}{dx} = \left(\frac{d^2y}{dx^2} + 2\right)^{1/2} + \frac{d^2y}{dx^2} + 5$ are respectively