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If y= A sin x+ B cos x, then prove that ...

If `y= A sin x+ B cos x`, then prove that `(d^2y)/(dx^2)+y=0`.

Text Solution

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y=Asinx+Bcosx
differentiate with respect to x
`y'(x)`=Acosx-Bsinx
differentiate with respect to x
`y''(x)`=-Asinx-Bcosx
`y''(x)`=-(Asinx+Bcosx)
`y''(x)`=-y
`y''(x)`+y=0
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