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

Category: QuestionsThe function y=3 cos⁡x is a solution of the function \frac{d^2 y}{dx^2}-3\frac{dy}{dx}=0.
Editor">Editor Staff asked 11 months ago

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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options
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Editor">Editor Staff answered 11 months ago

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.