Question

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

Answer 1

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.