1.

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) FalseThis 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»

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.


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