Given y=Acos⁡(kt)+Bsin⁡(kt) where A,B,k are constants, prove that y(2)+(k2)y=0 There was a silly typo, yn...

siutulysr5

siutulysr5

Answered

2022-01-26

Given y=Acos(kt)+Bsin(kt) where A,B,k are constants, prove that y(2)+(k2)y=0
There was a silly typo, yn is actually y′′

Answer & Explanation

Amina Hall

Amina Hall

Expert

2022-01-27Added 11 answers

y=d2dt2y=ddt({ddty})=ddt(Aksin(kt)+Bkcos(kt))=kddt(Asin(kt)+Bcos(kt))=
k2(Acos(kt)Bsin(kt))=k2y
may be the derivatives of sin(x) and cos(x)

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