List of top Mathematics Questions on Order and Degree of a Differential Equation

The sum of the order and the degree of the differential equation \(\left[\frac{d^2y}{dx^2}\right]^2 + \left[\frac{dy}{dx}\right]^4 + 3\left(\frac{dy}{dx}\right) + 1 - y^2 = 0\) is:

Identify the order and degree of the differential equation: \[ \left(\frac{d^3y}{dx^3}\right)^2 + 4\left(\frac{dy}{dx}\right)^4 + y = \sin(x) \]

Determine the sum of the order and the degree of the differential equation given by: \[ y = x\frac{dy}{dx} + \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \]

Determine the sum of the order and the degree of the following differential equation: \[ \left[1 + \left(\frac{dy}{dx}\right)^2\right]^{frac{3}{2}} = k \frac{d^2y}{dx^2} \]

The sum of order and degree of the differential equation \[ y=x\frac{dy}{dx}+2\sqrt{1+\left(\frac{dy}{dx}\right)^2} \] is:

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is: