Explanation

(b)
Given equation is $\ y = ax^{n + 1} + bx^{- n}$
On differentiating with respect to $x$, we get
$\frac{dy}{dx} = a(n + 1)x^{n} - bnx^{- n - 1}$
Again, on differentiating , we get
$\frac{d^{2}y}{dx^{2}} = an(n + 1)x^{n - 1} + bn(n + 1)x^{- n - 2}$
$\Rightarrow x^{2}\frac{d^{2}y}{dx^{2}} = an(n + 1)x^{n + 1} + bn(n + 1)x^{- n}$
$\Rightarrow x^{2}\frac{d^{2}y}{dx^{2}} = n(n + 1)(ax^{n + 1} + bx^{- n})$
$\Rightarrow \ \frac{{x^{2}d}^{2}y}{dx^{2}} = n(n + 1)y$