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

The order of the differential equation of all parabolas having their directrix parallel to the $x$-axis is

The difference of the order and degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^{-\frac{7}{2}}\left(\frac{d^3 y}{d x^3}\right)^2-\left(\frac{d^2 y}{d x^2}\right)^{-\frac{5}{2}}\left(\frac{d^4 y}{d x^4}\right)=0$ is

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

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

For the differential equation $\frac{d^3y}{dx^3} + \cos \left( \frac{d^2y}{dx^2} \right) = 0$, which of the following is true?