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If y=Acosn x+Bsinn x , show that (d^2y)/...

If `y=Acosn x+Bsinn x ,` show that `(d^2y)/(dx^2)+n^2\ y=0` .

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We have given that
`y=Acosnx+Bsinnx`
`(dy)/(dx)=An(-sinnx)+Bn(cosnx)`
`(d^2y)/(dx^2)=−n^2Acosnx+n^2B(−sinx)`
`(d^2y)/(dx^2)=−n^2(Acosnx+Bsinnx)`
`(d^2y)/(dx^2)+n^2y=0`
Hence Proved.
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RD SHARMA-HIGHER ORDER DERIVATIVES-Solved Examples And Exercises
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