Question

The non-linear differential equation from the following options is

• A. $\frac{d^2y}{dx^2} + \frac{dy}{dx} + 10y = 0$
• B. $\frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^2 + 10y = 0$
• C. $\frac{d^2y}{dx^2} + \frac{dy}{dx} + 10x = 0$
• D. $\frac{d^2y}{dx^2} + \frac{dy}{dx} + 10xy = 0$

Hint:

A differential equation is considered non-linear if any of the terms involving the dependent variable or its derivatives are raised to a power other than 1.

Answer 1

The Correct Option is B

- A non-linear differential equation contains terms in which the dependent variable or its derivatives appear with exponents other than 1, such as $\left(\frac{dy}{dx}\right)^2$.
- In option (B), the term $\left(\frac{dy}{dx}\right)^2$ makes the equation non-linear. Hence, the correct answer is (B).