Prove that an autonomous ODE $f(x)=x'$ has no nonconstant periodic solutions.
I guess I could prove it by contradiction by saying $x(t+T) = x(t)$ implies $x(t) =$ constant.
Prove that an autonomous ODE $f(x)=x'$ has no nonconstant periodic solutions.
I guess I could prove it by contradiction by saying $x(t+T) = x(t)$ implies $x(t) =$ constant.