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

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

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

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

If y= e^(a cos^(-1)x), -1 le x le 1 , show that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-a^(2)y=0 .

If y= (tan^(-1)x)^2, then show that (1+x^2)^2(d^2y)/(dx^2)+2x(1+x^2)(dy)/(dx) =2 .

answer the foll. Questions: (i) if y=(sin^(-1)x)/(sqrt(1-x^2)) , then show that (1-x^2) (d^2y)/dx^2-3x dy/dx -y=0

If y=e^(acos^(-1)x),-1lt=x<1,s how t h a t (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)-a^2y=0

If y="("x+sqrt(x^(2)-1)")"^(m) , then prove that, (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)+m^(2)y=0

Let y = (sin^(-1)x)^2+(cos^(-1)x)^2 show that (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)=4

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