Question

lf $y=\sin \left(7{\sin }^{-1}x\right)$ then $(1-x^2)y^{\prime \prime }-x{y}^{\prime }=$

• A. $-49y$
• B. $-7y$
• C. $49y$
• D. $7y$

Answer 1

The correct option is A $-49y$

$\frac{dy}{dx}=-\sin \left(7{\sin }^{-1}x\right)\frac{7}{\sqrt{1-x^2}}$

$\frac{d^{2}y}{d{x}^2}=-\cos \left(7{\sin }^{-1}x\right)\frac{7}{(1-x^2)}+\frac{-\sin \left(7{\sin }^{-1}x\right)7(-x)}{(\sqrt{1-x^2}{)}^3}$

$\frac{d^{2}y}{d{x}^2}=\frac{-7^{2}y}{1-x^2}+\frac{x{y}^{\prime }}{1-x^2}$

$(1-x^2)y^{\prime \prime }-x{y}^{\prime }=-49y$