If `y =(sin^(-1) x)^2`, prove that
`(1-x^2)y_2 - xy_1 - 2 = 0`

If y = tan^(-1) x, prove that (1 + x^2)y_2 + 2xy_1 = 0

If y = sin(mcos^(-1)x) then prove that (1-x^(2))y_(2)-xy_(1)+m^(2)y=0 .

If y= tan^-1 x then prove that (1+x^2) y_(2) + 2xy_(1) =0. Differentiate sec^-1(1/(2x^2 -1)) with respect to sqrt 1-x^2 .

If y=(sin^(-1)x)/(sqrt(1-x^(2))) , the prove that (1-x^(2))(d^(2)y)/(dx^(2))-3x(dy)/(dx)-y=0 .

If y = ax sin x show that x^2y_2 - 2xy_1 + (x^2 + 2)y = 0

If x =sin t,y = sin 2t then prove that (1-x^2)(d^2y)/(dx^2)- x dy/dx + 4y = 0

If y^(1//m)+y^(-1//m)=2x , then prove that (x^(2)-1)y_(2)+xy_(1)=m^(2)y^(2)

(i) If x=sin t , y=sin 2t then prove that (1-x^2)d^2y/dx^2-xdy/dx+4y=0 . If y=gof (x) then find dy/dx.

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

If sin^(-1) x +sin^(-1) y + sin^(-1) z =pi , "show that" x sqrt(1-x^2)+y sqrt(1-y^2) +zsqrt(1-z^2)=2 xyz