If `y^3-y=2x ,t h e n(x^2-1/(27))(d^2y)/(dx^2)+x(dy)/d=` `y` b. `y/3` c. `y/9` d. `y/(27)`

If y=2x^(n+1)+3xn ,then x^2d^2y/dx^2 is

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

If y^2=P(x) , then 2d/dx(y^3(d^2y/dx^2))

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

If x y+y^2=tanx+y ,t h e n(dy)/(dx)dot

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

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0 . Hence find y_(2) when x=0

(a+bx)e^(y/x)=x , Prove that x^3(d^2y)/(dx^2)=(x(dy)/(dx)-y)^2

If y= (cos^(-1) x)^2 , prove that (1-x^2) (d^2y)/(dx^2) - x(dy)/(dx) -2 =0 , Hence find y_2 when x=0 .