Question

Based on the differential equation \[\left(\frac{d^{3}y}{dx^{3}}\right)^{2} + 5\frac{dy}{dx} = \sin(x)\], what is the degree?

Options

• Degree = 2

• Degree = 1

• Degree = 5

• Degree = 3

Answer 1

The degree is the highest exponent of the highest derivative. The highest order derivative \[\frac{d^{3}y}{dx^{3}}\] appears with an exponent of 2 in the term \[\left(\frac{d^{3}y}{dx^{3}}\right)^{2}\]. Therefore, the degree is 2.