1.

Verify that `y = A cos x - Bsin x` is a solution of the differential equation `(d^2y)/(dx^2)+y=0`

Answer» Given: `y=A cos x-B sin x`
`implies(dy)/(dx)=-A sinx-B cos x`
`implies (d^(2)y)/(dx^(2))=-Acosx+Bsinx`
`=-(A cosx-Bsinx)=-y" "["from (i)"]`
`implies(d^(2)y)/(dx^(2))+y=0.`
Hence, `y=Acos x-Bsinx` is a solution of the differential equation `(d^(2)y)/(dx^(2))+y=0.`


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