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}} $

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

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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from STD 12 - 5. continuity and differentiation→STD 12 - 5. continuity and differentiation — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

The differential equation of all circles passing through the origin and having their centres on the $x-$axis is

Choose the correct answer from given four options in each of the Exercise: If $\text{A}=\begin{vmatrix}2&\lambda&-3\\0&2&5\\1&1&3\end{vmatrix},$ then $A^{-1}$ exists, if:

If $A = \left[ {\begin{array}{*{20}{c}}i&0\\0&i\end{array}} \right]$ and $B = \left[ {\begin{array}{*{20}{c}}0&{ - i}\\{ - i}&0\end{array}} \right]$, then $(A + B)(A - B)$ is equal to

$\int\sqrt{\frac{\text{x}}{1-\text{x}}}\text{ dx}$ is equal to:

Find the principal value of $\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)$

If $a, b, c$ are any three vectors and their inverse are ${a^{ - 1}},\,{b^{ - 1}},\,{c^{ - 1}}$ and $[a\,b\,c] \ne 0,$ then $[{a^{ - 1}}\,{b^{ - 1}}\,{c^{ - 1}}]$ will be

For a real number $\alpha$, if the system

$\left[\begin{array}{ccc}1 & \alpha & \alpha^2 \\ \alpha & 1 & \alpha \\ \alpha^2 & \alpha & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{c}1 \\ -1 \\ 1\end{array}\right]$

of linear equations, has infinitely many solutions, then $1+\alpha+\alpha^2=$

If $\int_{}^{} {\frac{1}{{(\sin x + 4)(\sin x - 1)}}\;dx = A\frac{1}{{\tan \frac{x}{2} - 1}} + B{{\tan }^{ - 1}}(f(x))} + C$, then

For $m, n > 0$, let $\alpha(m, n)=\int_0^2 t^m(1+3 t)^n d t$. If $11 \alpha(10,6)+18 \alpha(11,5)= p (14)^6$, then $p$ is equal to $......$.

let $S = \{1, 2, … 20\}$. A subset $B$ of $S$ is said to be $“nice”$, if the sum of the elements of $B$ is $203$. Then the probability that a randomly chosen subset of $S$ is $‘nice’$ is