Question

Find the order and degree of the following differential equation: \[ \frac{d^3 y}{dx^3} + \frac{d^2 y}{dx^2} + \frac{dy}{dx} + y = 0 \]

Hint:

In differential equations, the order refers to the highest derivative, while the degree refers to the power of the highest derivative.

Answer 1

The order of the differential equation is the highest derivative, which is \( \frac{d^3 y}{dx^3} \), so the order is 3. The degree of the differential equation is the highest power of the highest derivative, which is 1. Thus, the order is 3 and the degree is 1.