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If y=5" cos"x-3" sin"x, prove that (d^(2...

If `y=5" cos"x-3" sin"x`, prove that `(d^(2)y)/(dx^(2))+y=0.`

Text Solution

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`y=5" cos"x-3" sin"x`
`implies(dy)/(dx)=(d)/(dx)(5" cos"x-3" sin"x)= -5sinx-3cos x`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)(-5" sin"x-3 cos x)`
`= -5 cos x+3 sin x `
`= -(5 cos x-3 sin x)= -y`
`implies(d^(2)y)/(dx^(2))+y=0 " " `Hence Proved.
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