If y-ax-n-1-bx-n- then x-2-y-ny-n-1-y-n-n-1-yn-n-1-y

Question

Toppr Admin · Accepted Answer

Y-x2032-n-1-axn-x2212-nbx-x2212-n-x2212-1y-x2032-x2032-n-n-1-axn-x2212-1-n-n-1-bx-x2212-n-x2212-2x2y-x2032-x2032- -n-n-1-axn-1-n-n-1-bx-x2212-n-n-n-1-axn-1-bx-x2212-n-n-n-1-y

If $y = a x^{n + 1} + b x^{- n}$ then $x^{2} y^{''} =$

$n y$
$(n + 1) y$
$- n (n + 1) y$
$n (n + 1) y$

$y^{'} = (n + 1) a x^{n} - n b x^{- n - 1}$
$y^{''} = n (n + 1) a x^{n - 1} + n (n + 1) b x^{- n - 2}$
$x^{2} y^{''}$ $= n (n + 1) a x^{n + 1} + n (n + 1) b x^{- n} = n (n + 1) (a x^{n + 1} + b x^{- n}) = n (n + 1) y$

If y=axn+1+bx−n then x2y′′=ny(n+1)y−n(n+1)yn(n+1)y

y′=(n+1)axn−nbx−n−1y′′=n(n+1)axn−1+n(n+1)bx−n−2x2y′′ =n(n+1)axn+1+n(n+1)bx−n=n(n+1)(axn+1+bx−n)=n(n+1)y

If $y = a x^{n + 1} + b x^{- n}$ then $x^{2} y^{''} =$

$n y$
$(n + 1) y$
$- n (n + 1) y$
$n (n + 1) y$

$y^{'} = (n + 1) a x^{n} - n b x^{- n - 1}$
$y^{''} = n (n + 1) a x^{n - 1} + n (n + 1) b x^{- n - 2}$
$x^{2} y^{''}$ $= n (n + 1) a x^{n + 1} + n (n + 1) b x^{- n} = n (n + 1) (a x^{n + 1} + b x^{- n}) = n (n + 1) y$