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

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^3+\left(\frac{d y}{d x}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ is . . . . . . .

The number of arbitrary constants in a particular solution of a differential equation is . . . . . . .

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 $\sqrt{1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{3/2}$ are respectively:

The order and degree of the differential equation $\left[1+\frac{1}{(\frac{dy}{dx})^{2}}\right]^{\frac{5}{3}}=5 \frac{d^{2}y}{dx^{2}}$ are respectively: