# Math Help - Find the function

1. ## Find the function

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.
$x^{,}_{1}=x_{1}+ax_{2}+sin(ax_{1})$
$x_1(0)=1$
$x^{,}_{2}=x_{2}-ax_{1}+cos(ax_{2})$
$x_{2}(0)=0\\$
Show that any staturated answers are defined for any $t \in R$. Find $\frac{\partial x}{\partial a}\ for\ a=0\ where\ x=(x_{1},x_{2})$