Question

Which of the following is a linear differential equation

• A. $\left( \frac{d^{2}y}{dx^{2}} \right)^{2} + x^{2}\left( \frac{dy}{dx} \right)^{2} = 0$
• B. $y = \frac{dy}{dx} + \sqrt{1 + \left( \frac{dy}{dx} \right)^{2}}$
• C. $\frac{dy}{dx} + \frac{y}{x} = \log x$
• D. $y\frac{dy}{dx} - 4 = x$

Answer 1

Answer: (C)

$\frac{dy}{dx} + \frac{y}{x} = \log x$

Answer 2

(1), (2), (4) do not fulfill the criteria of a linear

differential equation but (3) do.

$\frac{dy}{dx} + \frac{y}{x} = \log x$ is a linear differential equation.