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

(a) y=5 cos3x

(b) y=5 tan3x

(c) y=cos3x

(d) y=6 cos3x

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

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The correct choice is (a) y=5 cos3x

The explanation: Consider the function y=5 cos3x

Differentiating w.r.t x, we get

y’=

dy

dx

=-15 sin3x

Differentiating again w.r.t x, we get

y”=

d

2

y

d

x

2

=-30 cos3x

⇒y”+6y=0.

Hence, the function y=5 cos3x is a solution for the differential equation y”+6y=0.