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
 
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
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
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1 Answers
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.