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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1 Answers
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.