यदि `y=sin^(-1)x,` सिद्ध कीजिए : `(1-x^(2))(d^(2)y)/(dx^(2))=x(dy)/(dx)`

If y= sin (8 sin ^(-1) x ) then (1-x ^(2)) (d^(2)y)/(dx ^(2))-x (dy)/(dx)=- ky, where k =

y^2+x^2(dy)/(dx)=x y(dy)/(dx)

If y=e^("mcos"^(-1)x) , prove that: (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=m^(2)y

If y=e^(m"sin"^(-1)x) , prove that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/(dx)=m^(2)y

If y=sin^(-1)x , then show that (1-x^2)\ (d^2y)/(dx^2)-x(dy)/(dx)=0 .

If logy=tan^(-1)x , prove that : (1+x^(2)) (d^(2)y)/(dx^(2))+(2x-1)(dy)/(dx)=0

If y=sin^(-1)x , show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=0 .

If e^y(x+1)=1, show that (d^(2y))/(dx^2)=((dy)/(dx))^2 If y=sin(2sin^(-1)x), show that ((1-x^2)d^(2y))/(dx^2)=x(dy)/(dx)-4y

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

If x=costheta,y=sin5theta," then "(1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)=