Question

Which of the following functions is the solution of the differential equation \(\frac{dy}{dx}\)+2y=0?

(a) y=-2e^-x

(b) y=2e^x

(c) y=e^-2x

(d) y=e^2x

I got this question during an internship interview.

The above asked question is from General and Particular Solutions of Differential Equation topic in division Differential Equations of Mathematics – Class 12

Answer 1

Right choice is (c) y=e^-2x

Easy explanation: Consider the function y=e^-2x

Differentiating both sides w.r.t x, we get

\(\frac{dy}{dx}=-2e^{-2x}\)

\(\frac{dy}{dx}\)=-2y

⇒\(\frac{dy}{dx}\)+2y=0.