Question

The function y=3 cos⁡x is a solution of the function \(\frac{d^2 y}{dx^2}-3\frac{dy}{dx}\)=0.

(a) True

(b) False

This question was posed to me during an internship interview.

Enquiry is from General and Particular Solutions of Differential Equation topic in chapter Differential Equations of Mathematics – Class 12

Answer 1

Correct choice is (b) False

The best explanation: The given statement is false.

Given differential equation: \(\frac{d^2 y}{dx^2}\)-3 \(\frac{dy}{dx}\)=0 –(1)

Consider the function y=3 cos⁡x

Differentiating w.r.t x, we get

\(\frac{dy}{dx}\)=-3 sin⁡x

Differentiating again w.r.t x, we get

\(\frac{d^2 y}{dx^2}\)=-3 cos⁡x

Substituting the values of \(\frac{dy}{dx}\) and \(\frac{d^2 y}{dx^2}\) in equation (1), we get

\(\frac{d^2 y}{dx^2}\)-3 \(\frac{dy}{dx}\)=-3 cos⁡x-3(-3 sin⁡x)

=9 sin⁡x-3 cos⁡x≠0.

Hence, y=3 cos⁡x, is not a solution of the equation \(\frac{d^2 y}{dx^2}\)-3 \(\frac{dy}{dx}\)=0.