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Show that the function y=A cos x+B sin x...

Show that the function `y=A cos x+B sin x\ ` is as solution of the differentia equation `(d^2y)/(dx^2)+y=0.`

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Given, `y=A cos x+b sin x\ `

Differentiating w.r.t. `x`

`y'=-Asinx+Bcosx`


Differentiating w.r.t. `x`

`y''=-Acosx-Bsinx`

`y''=-y`

`y''+y=0`


(Hence proved)
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