`y=(cot^(- 1)x)^2,t h e n s h o w t h a t(x^2+1)^2(d^2y)/(dx^2)+2x(x^2+1)(dy)/(dx)=2`

If y=(t a n^(-1)\ x)^2 , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(dy)/(dx)=2.

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

If y=sin^(-1)x , \ s how \ t h a t \ (d^2y)/(dx^2)=x/((1-x^2)^(3/2))

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

If e^y(x+1)=1,s howt h a t(d^2y)/(dx^2)=((dy)/(dx))^2dot

If x=sint ,y=sinp t ,"p r o v et h a t" (1-x^2)(d^2y)/(dx^2)-x(dy)/(dx)+p^2y=0.

If y=cos^(-1)(cosx),t h e n(dy)/(dx) is equal to x/y (b) y/(x^2) (x^2-y^2)/(x^2+y^2) (d) y/x

If y=xlog(x/(a+b x)),t h e nx^3(d^2y)/(dx^2)= (a) x(dy)/(dx)-y (b) (x(dy)/(dx)-y)^2 y(dy)/(dx)-x (d) (y(dy)/(dx)-x)^2