Maths Derivatives

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If y = x ^ n + ( 1 / x ^ n )

prove that

( x^2y'' ) + ( xy' ) - ( n^2y ) = 0

  • Maths Derivatives -

    y = xn + x-n
    y' = nxn-1 - nx-n-1
    y'' = n(n-1)xn-2 + n(n+1)x-n-2

    x2y'' + xy' - n2y
    = n(n-1)xn + n(n+1)x-n + nxn - nx-n - n2xn - n2x-n
    = 0

  • Maths Derivatives -

    thank u so much
    i realised that i had the correct answer but wasn't sure about the signs

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