Résoudre les systèmes suivants :
1
\(\left\{ \begin{array}{l} x'=4x-2y\\ y'=x+y \end{array} \right.\)
2
\(\left\{ \begin{array}{l} x'=x-y+ \frac{1}{\cos t}\\ y'=2x-y \end{array} \right.\) sur \(\left]- \frac{\pi}{2}, \frac{\pi}{2}\right[\)
3
\(\left\{ \begin{array}{l} x'=5x-2y+e^t\\ y'=-x+6y+t \end{array} \right.\)
4
\(\left\{ \begin{array}{l} x'=5x+y-z\\ y'=2x+4y-2z\\ z'=x-y+z \end{array} \right.\)
5
\(\left\{ \begin{array}{l} x'=2x+y\\ y'=-x\\ z'=x+y+z \end{array} \right.\) (trouver la solution telle que \(x(0)=0\), \(y(0)=1\) et \(z(0)=-1\)).