Change of variables on autonomous systems solutions

[GlassBones]

Homework Statement

Given that $x=\phi (t)$, $y=\psi(t)$ is a solution to the autonomous system $\frac{dx}{dt}=F(x,y)$, $\frac{dy}{dt}=G(x,y)$ for $\alpha < t < \beta$, show that
$x=\Phi(t)=\phi(t-s)$, $y=\Psi(t)=\psi(t-s)$
is a solution for $\alpha+s<t<\beta+s$ for any real number s.

Homework Equations

The Attempt at a Solution

I noticed $\alpha+s<t<\beta+s \equiv \alpha<t-s<\beta$. I'm thinking to do change of variables. But don't really know how to do that.

Notation wise does this makes sense $\frac{dx}{d(t-s)}$.

 

[Orodruin]

Hint: Chain rule for derivatives.