Question

( y=frac{sin ^{-1} x}{sqrt{1-x^{2}}} )
( sqrt{1-x^{2} y=sin ^{-1} x} )
Differentiating both sides
( frac{-2 x y}{2 sqrt{1-x^{2}}+sqrt{1-x^{2}} frac{d y}{d x}=frac{1}{sqrt{1-x^{2}}}} )
( Rightarrow frac{-x y}{sqrt{1-x^{2}}+sqrt{1-x^{2}} y_{1}=frac{1}{sqrt{1-x^{2}}}} )
Differentiative again
( -y-y-x y_{1}-2 x y_{1}+left(1-x^{2}right) y_{2}=0 )
( Rightarrowleft(1-x^{2}right) y_{2}-3 x y_{1}-y=0 )
Heres, proved.

# | १. 4:17_ 1-७ । _ _ (1) -3303 =० ॥ 3-

Solution