\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-2 z \left (t \right )-3 x \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = -{\mathrm e}^{2 t}, y^{\prime }\left (t \right )+3 x \left (t \right )-2 y \left (t \right ) = 6 \,{\mathrm e}^{2 t}] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-\cos \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )-2 x \left (t \right )+\cos \left (t \right )+\sin \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = y \left (t \right )+\tan \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = \tan \left (t \right )-x \left (t \right )] \]

\[ {}\left [x^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+\frac {2}{{\mathrm e}^{t}-1}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )-\frac {3}{{\mathrm e}^{t}-1}\right ] \]

\[ {}\left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {1}{\cos \left (t \right )}\right ] \]

\[ {}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+1] \]

\[ {}[x^{\prime }\left (t \right ) = 3-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 t] \]

\[ {}[x^{\prime }\left (t \right ) = -y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\cos \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )+4 t -1, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+t] \]

\[ {}[x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right )+y \left (t \right ) = t^{2}, y^{\prime }\left (t \right )-x \left (t \right ) = t] \]

\[ {}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{-t}, 2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-2 z \left (t \right )+2-t, y^{\prime }\left (t \right ) = -x \left (t \right )+1, z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )+1-t] \]

\[ {}[x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 1, z^{\prime }\left (t \right )+z \left (t \right ) = 1] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 6 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+5 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+\sin \left (t \right )] \]