The order of the differential equation whose solution is ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is:

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 degree of the differential equation $ y = x \frac{dy}{dx} + \frac{2}{dy/dx} $ are

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

If the order and degree of the differential equation $x \frac{d^2 y}{d x^2} = \left(1 + \left(\frac{d^2 y}{d x^2}\right)^2\right)^{-1/2}$ are $k$ and $l$ respectively,then $k, l$ are the roots of

The number of arbitrary constants in the particular solution of a fourth-order differential equation is . . . . . . .