`y=e^xxxtan^(- 1)x ,s h o w t h a t(1+x^2)y_2-2(1-x+x^2)y_1+(1-x^2)y=0`

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

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 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 x=sin theta,y=cosptheta,p rov e \ t h a t (1-x^2)y_2-x y_1+p^2y=0,w h e r e \ y_2=(d^2y)/(dx^2) \ a n d \ y_1=(dy)/(dx)

If y=e^x , Prove that , xy_2-(2x-1)y_1+(x-1)y=0 .

If y=sqrt((1-x)/(1+x)),p rov et h a t(1-x^2)(dy)/(dx)+y=0