Given y=cotx

Then `(dy)/(dx)=-csc^2x`

and `(d^2y)/(dx^2)=-2cscx(-cscxcotx)=2csc^2xcotx`

So `(d^2y)/(dx^2)+2y(dy)/(dx)`

`=2csc^2xcotx+2cotx(-csc^2x)`

=0 as required.

Given y=cotx

Then `(dy)/(dx)=-csc^2x`

and `(d^2y)/(dx^2)=-2cscx(-cscxcotx)=2csc^2xcotx`

So `(d^2y)/(dx^2)+2y(dy)/(dx)`

`=2csc^2xcotx+2cotx(-csc^2x)`

=0 as required.