Question

Which ONE of the following is a linear non- homogenous differential equation, where x and y are the independent and dependent variables respectively?

• A. $\frac{dy}{dx}+xy=e^{-x}$
• B. $\frac{dy}{dx}+xy=0$
• C. $\frac{dy}{dx}+xy=e^{-y}$
• D. $\frac{dy}{dx}+e^{-y}=0$

Answer 1

The correct option is A $\frac{dy}{dx}+xy=e^{-x}$

(a) $\frac{dy}{dx}+xy=e^{-x}$ is first order non-homogeneous linear equation

(b) $\frac{dy}{dx}+xy=0$ is first order homogeneous linear equation

(c) (d) are non linear eq's.