If y = a x^ n + 1 + b x^ - n , then x^2 d^2 y d x^2 = - Vidyadip

MCQ

If $y = a{x^{n + 1}} + b{x^{ - n}}$, then ${x^2}{{{d^2}y} \over {d{x^2}}} = $

A
$n\,(n - 1)y$
✓
$n\,(n + 1)y$
C
$ny$
D
${n^2}y$

✓

Answer

Correct option: B.

$n\,(n + 1)y$

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

$\Rightarrow \frac{{dy}}{{dx}} = (n + 1)a{x^n} - nb{x^{ - n - 1}}$

==> $\frac{{{d^2}y}}{{d{x^2}}} = n(n + 1)a{x^{n - 1}} + n(n + 1)b{x^{ - n - 2}}$

==> ${x^2}\frac{{{d^2}y}}{{d{x^2}}} = n(n + 1)y$.

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