The number of arbitrary constants in the particular solution of a differential equation of third order are . . . . . . .

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

Determine the order and degree (if defined) of the differential equation $y''' + 2y'' + y' = 0$.

The order and degree of the differential equation $3 - (\frac{d^3y}{dx^3})^{2/3} = (\frac{dy}{dx})^5$ are respectively

The order and degree of the differential equation $(\frac{d^3y}{dx^3}+y\frac{dy}{dx})^{\frac{7}{5}} =x^3\frac{d^2y}{dx^2}$ are $m$ and $n$ respectively,then $(m + n)$ is equal to-

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