Question

Which of the following differential equation is linear ?

• A. $\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}+2y=0$
• B. $\frac{d^{2}y}{d{x}^2}+y\frac{dy}{dx}+x=0$
• C. $\frac{d^{2}y}{d{x}^2}+\frac{y}{x}+\sin y=x^2$
• D. $(1+x)\frac{dy}{dx}-xy=1$

Answer 1

The correct option is D $(1+x)\frac{dy}{dx}-xy=1$

Only in the equation $(1+x)\frac{dy}{dx}-xy=1$ , both the terms $\frac{dy}{dx}$ and $y$ are linear. Hence this equation is a linear differential equation.