IF `y^(2)(1-x^(2))=x^(2)+1`, show that, `(1-x^(4))((dy)/(dx))^(2)=y^(4)-1`.

If y=(x sin^(-1)x)/(sqrt(1-x^(2)))+log sqrt(1-x^(2)) , show that, (1-x^(2))^(2)(D^(2)y)/(dx^(2))-3x(1-x^(2)))(dy)/(dx)=1

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

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

(1+x^(2))(dy)/(dx)+y=e^(tan^(-1)x)

If x^(2)+y^(2)=t-(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)) , show that, x^(3)y(dy)/(dx)=1

y(1-x^(2))dy=x(1+y^(2))dx

If y=((1+x)/(1-x))^(n) , prove that (1-x^(2))(d^(2)y)/(dx^(2))=2(n+x)(dy)/(dx).

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

If y sqrt(x^(2)+1)=log(sqrt(x^(2)+1)-x) , show that, (x^(2)+1)(dy)/(dx)+xy+1=0

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