Prove that the function: y (x) = A cosx + B sin x (A and B are constants), is a solution to the differential equation.

Question

Mathematics

Emerson Daugherty

10 November, 19:05

Prove that the function: y (x) = A cosx + B sin x (A and B are constants), is a solution to the differential equation.

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Answers (1)

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Esparza · Answer 1

Step-by-step explanation:

y=A cos x+B sin x

y'=-A sin x+B cos x

y''=-Acos x-B sin x = - (A cos x+B sin x) = -y

so y''=-y

y''+y=0

which is the reqd. diff. equation.