Question

In the differential equation \[\frac{d^{2}y}{dx^{2}} + \left(\frac{dy}{dx}\right)^{3} - y = 0\], what are the order and degree respectively?

Options

• Order = 1, Degree = 3

• Order = 3, Degree = 2

• Order = 2, Degree = 3

• Order = 2, Degree = 1

Answer 1

The highest order derivative is \[\frac{d^{2}y}{dx^{2}}\] (second-order), so the order is 2. The highest exponent of the highest derivative is 1 (the \[\frac{d^{2}y}{dx^{2}}\] term appears to the power 1). Therefore, the degree is 1. The cubic term \[\left(\frac{dy}{dx}\right)^{3}\] is a lower-order derivative.