Show that `y=(c-x)/(1+c x)` is a solution of the different equation `(1+x^2)dy/(dx)+(1+y^2)=0.`

Explanation

`y=(c-x)/(1+c x)`


`y(1+cx)=c-x`


`y'(1+cx)+y(c)=-1`


`y'=(-1-cy)/(1+cx)`


`y'=(-1-c((c-x)/(1+c x)))/(1+cx)`


`y'=(-(1+cx)-c^2+cx)/(1+cx)^2`


`y'=(-1-c^2)/(1+cx)^2`


Now,


...