If y = sin(m sin^{-1} x),then (1 - x^2) y_2 - | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $y = \sin(m \sin^{-1} x)$.Differentiating with respect to $x$:$y_1 = \cos(m \sin^{-1} x) \cdot \frac{m}{\sqrt{1 - x^2}}$$y_1 \sqrt{1 - x^2}

Vedclass · Accepted Answer

$-m^2 y$

Vedclass · Answer

(B) Given $y = \sin(m \sin^{-1} x)$.Differentiating with respect to $x$:$y_1 = \cos(m \sin^{-1} x) \cdot \frac{m}{\sqrt{1 - x^2}}$$y_1 \sqrt{1 - x^2} = m \cos(m \sin^{-1} x)$Squaring both sides:$y_1^2 (1 - x^2) = m^2 \cos^2(m \sin^{-1} x) = m^2 (1 - \sin^2(m \sin^{-1} x)) = m^2 (1 - y^2)$$y_1^2 (1 - x^2) = m^2 - m^2 y^2$Differentiating again with respect to $x$:$2 y_1 y_2 (1 - x^2) + y_1^2 (-2x) = -2 m^2 y y_1$Dividing by $2 y_1$ (assuming $y_1 
eq 0$):$y_2 (1 - x^2) - x y_1 = -m^2 y$

If $y = \sin(m \sin^{-1} x)$,then $(1 - x^2) y_2 - x y_1$ is equal to (Here,$y_n$ denotes $\frac{d^n y}{dx^n}$)

Similar Questions

$A$ particle of mass $m$ is located in a one-dimensional potential field where the potential energy is given by: $V(x) = A(1 - \cos px)$,where $A$ and $p$ are constants. The period of small oscillations of the particle is:

How many bridging oxygen atoms are present in $P_4O_{10}$?

Identify the correct decreasing order of the following with respect to altitude from the atmosphere:
$I$. Troposphere
$II$. Mesosphere
$III$. Thermosphere

Which of the following types of cell junctions is not found in animal tissues?

Alkali metals lose electrons from which orbitals?

Vedclass Test Series

Exam Paper Generator

Online Exam Module