Question

Sol. ( quad y=left(sin ^{-1} xright)^{2} )
rentiaturg bofh sides
( int 1-x^{2} frac{d y}{d x}=2 sin ^{-1} x+x )
Díforentiating breth sides-
( sqrt{1-x^{2}} frac{d^{2} y}{d x^{2}}+frac{d y}{d x}left(frac{(-2 x)}{2 sqrt{1-x^{2}}}right)=frac{2}{sqrt{1-x^{2}}}+0 )
( left(1-x^{2}right) frac{d^{2} y}{d x^{2}}+frac{d y}{d x}(-x)=2 )
8
( left(1-x^{2}right) frac{d^{2} y}{d x^{2}}-frac{x d y}{d x}-2=0 )
hemce proved: ( left[left(1-x^{2}right) frac{d^{2} y}{d x^{2}}-frac{x d y}{d x}=2right. )

# V dx is called the nth order derivative of y with respect tox. oy-1 illustration 1: If y= (sin "x+ k sin"x, show that (1 – x2) dy-xay = 2. dy? dx Solution: Here v = (sin-12

Solution