If `y = e^(m cos^(-1) x)
(1-x^2)y_2-xy_1 = m^2y`

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

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

If y=e^(m sin ^(-1)x) , then show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-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=(log x)^(cos x)+(x^2+1)/(x^2-1) find (dy)/(dx) .

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

Find dy/dx y = cos^(-1)(1-1/x-1/x^(2))^(1/2)

x^n - y^n = (x-y) (x^(n-1) + x^(n-2) y + … + xy^(n-2) + y^(n-1)) , x,y in R