Question

Write the degree of the differential equation \( \frac{d^2y}{dx^2} + \frac{dy}{dx} = x \).

Hint:

The degree of a differential equation is found by identifying the highest power of the highest order derivative after simplifying the equation.

Answer 1

The given differential equation is: \[ \frac{d^2y}{dx^2} + \frac{dy}{dx} = x \] The degree of a differential equation is the highest power of the highest order derivative after making the equation free from derivatives in fractions or irrational powers. Here, the highest order derivative is \( \frac{d^2y}{dx^2} \), and its power is 1. Thus, the degree of the differential equation is: \[ \boxed{1} \]