We saw in class how to use Picard's successive approximation method to approximate a solution for an ODE by "guessing" $\Phi_0$ and then improving the guess using the formula: $\Phi_{n+1}(x) = \int_{0}^{x}f[t, \Phi_n(t)]dt$ Until now I only saw it applied to simple first-order differential equations, but now I have a system of linear equations: $ \left\{\begin{matrix} \dot{x} = y\\ \dot{y} = -x - \frac{8}{5}y \end{matrix}\right. $ For which I'm supposed to calculate approximations using this method. How can I do that?
Thanks!