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

Category: QuestionsWhich of the following functions is a solution for the differential equation y”+6y=0?
Editor">Editor Staff asked 11 months ago

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

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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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Editor">Editor Staff answered 11 months ago

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’=
dy
dx
=-15 sin⁡3x

Differentiating again w.r.t x, we get

y”=
d
2
y
d
x
2
=-30 cos⁡3x

⇒y”+6y=0.

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