Determine the order and degree (if defined) of the differential equation $\frac{d^4y}{dx^4} + \sin(y''') = 0$.

The degree of the differential equation $x = 1 + \left(\frac{dy}{dx}\right) + \frac{1}{2!} \left(\frac{dy}{dx}\right)^2 + \frac{1}{3!} \left(\frac{dy}{dx}\right)^3 + \dots$ is:

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

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 sum of the squares of the order and degree (if defined) of the differential equation $2y' + (y'')^2 = \sqrt{y'' - 3}$ is

The order and degree of the differential equation of all tangent lines to the parabola $x^2 = 4y$ are respectively: