Hello! I have a very nice exercise and don't now what to do. Anyone can to resolve this?

Ex

Consider this equations with parametr a.

$\displaystyle x^{,}_{1}=x_{1}+ax_{2}+sin(ax_{1})$

$\displaystyle x_1(0)=1$

$\displaystyle x^{,}_{2}=x_{2}-ax_{1}+cos(ax_{2})$

$\displaystyle x_{2}(0)=0\\$

Show that any staturated answers are defined for any $\displaystyle t \in R$. Find $\displaystyle \frac{\partial x}{\partial a}\ for\ a=0\ where\ x=(x_{1},x_{2})$