Question

Which of the following functions is a solution for the differential equation y”+6y=0?

(a) y=5 cos⁡3x

(b) y=5 tan⁡3x

(c) y=cos⁡3x

(d) y=6 cos⁡3x

This question was posed to me in an online quiz.

I need to ask this question from General and Particular Solutions of Differential Equation topic in section Differential Equations of Mathematics – Class 12

Answer 1

The correct choice is (a) y=5 cos⁡3x

The explanation: Consider the function y=5 cos⁡3x

Differentiating w.r.t x, we get

y’=\(\frac{dy}{dx}\)=-15 sin⁡3x

Differentiating again w.r.t x, we get

y”=\(\frac{d^2 y}{dx^2}\)=-30 cos⁡3x

⇒y”+6y=0.

Hence, the function y=5 cos⁡3x is a solution for the differential equation y”+6y=0.