Question

If $y=\sin \left(4{\sin }^{-1}x\right)$ satisfies the relation $(1-x^2)(y_2-x{y}_1)+Ay=0$ then the value of A is

Answer 1

$y=\sin \left(4{\sin }^{-1}x\right)..\left(1\right)$
$y_1=\cos \left(4{\sin }^{-1}x\right).\frac{4}{\sqrt{1-x^2}}..\left(2\right)$
$y_2=-\sin \left(4{\sin }^{-1}x\right).\frac{16}{1-x^2}+\cos \left(4{\sin }^{-1}x\right).\frac{x}{\sqrt{1-x^2}}$
$y_2=-\frac{16y}{1-x^2}+y_{1}x\Rightarrow (1-x^2)(y_2-x{y}_1)+16y=0$