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

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

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 .

Solve y^(2)+x^(2)(dy)/(dx)=xy(dy)/(dx)

If y= 3e^(2x)+2e^(3x) , prove that (d^(2)y)/(dx^(2))-5(dy)/(dx)+6y=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

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 = Ae^(6x) +Be^(-x) prove that (d^(2)y)/(dx^(2)) - 5 (dy)/(dx) - 6y = 0