Consider the autonomous system

$\displaystyle \frac{dx}{dt}=F(x, y),\ \frac{dy}{dt}=G(x, y)$

in a region where the functions $\displaystyle F$ and $\displaystyle G$ are continuously differentiable.

Suppose that $\displaystyle (x(t), y(t))$ is a solution of the system and that $\displaystyle \gamma\neq 0$. Define $\displaystyle \phi(t)=x(t+\gamma)$ and $\displaystyle \psi(t)=y(t+\gamma)$. Then show that $\displaystyle (\phi(t), \psi(t))$ is also a solution of the system.

:My attempt

$\displaystyle (x(t), y(t))$ is a solution of the autonomous system.

So, $\displaystyle x'(t)=F(x(t), y(t))$ and $\displaystyle y'(t)=G(x(t), y(t))$.

$\displaystyle \frac{d\phi(t)}{dt}=x'(t+\gamma)$

$\displaystyle \frac{d\psi(t)}{dt}=y'(t+\gamma)$

How do I proceed?