The function y=3 cosx is a solution of the function \frac{d^2 y}{dx^2}-3\frac{dy}{dx}

=0.

(a) True

(b) False

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

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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 cosx

Differentiating w.r.t x, we get

\frac{dy}{dx}

=-3 sinx

Differentiating again w.r.t x, we get

\frac{d^2 y}{dx^2}

=-3 cosx

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 cosx-3(-3 sinx)

=9 sinx-3 cosx≠0.

Hence, y=3 cosx, is not a solution of the equation \frac{d^2 y}{dx^2}

-3 \frac{dy}{dx}

=0.