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