Question

Which of the following functions is a solution for the differential equation \(\frac{dy}{dx}\)-14x=0?

(a) y=7x^2

(b) y=7x^3

(c) y=x^7

(d) y=14x

The question was posed to me during an online exam.

Question is taken from General and Particular Solutions of Differential Equation in portion Differential Equations of Mathematics – Class 12

Answer 1

Correct option is (a) y=7x^2

Easiest explanation: Consider the function y=7x^2

Differentiating w.r.t x, we get

\(\frac{dy}{dx}\)=14x

∴\(\frac{dy}{dx}\)-14x=0

Hence, the function y=7x^2 is a solution for the differential equation \(\frac{dy}{dx}\)-14x=0