Question

For the differential equation \[xy \frac{d^{2}y}{dx^{2}} + x \left( \frac{dy}{dx} \right)^{2} - y \frac{dy}{dx} = 0\], what is the degree?

Options

• Degree = 1

• Degree is not defined

• Degree = 3

• Degree = 2

Answer 1

The degree is the highest exponent of the highest derivative. The highest derivative \[\frac{d^{2}y}{dx^{2}}\] appears with an exponent of 1 in the term \[xy \frac{d^{2}y}{dx^{2}}\]. Since the equation is polynomial in its derivatives, the degree is 1.