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

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

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+z \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right )-t +3, y^{\prime }\left (t \right ) = -x \left (t \right )-5 y \left (t \right )+t +1] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+8 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )-9 z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 10 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right )+t -1, y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )-3 t^{2}, z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )+t^{2}-t +2] \]

\[ {}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )+{\mathrm e}^{-t} \sin \left (2 t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+9 z \left (t \right )+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ), z^{\prime }\left (t \right ) = y \left (t \right )+6 z \left (t \right )-{\mathrm e}^{-t}] \]

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

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )-9 z \left (t \right )-8 \,{\mathrm e}^{-2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{5 t}, z^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right )+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t}] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+{\mathrm e}^{-t}-3 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+2 \,{\mathrm e}^{-t}+t, z^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )+6 z \left (t \right )+2 \,{\mathrm e}^{-t}-t] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t}] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )] \]

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )] \]

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

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

\[ {}\left [x^{\prime }\left (t \right ) = -\frac {5 x \left (t \right )}{2}+2 y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-2 y \left (t \right )\right ] \]

\[ {}[x^{\prime }\left (t \right ) = 10 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-12 y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+10 y \left (t \right )+4 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )+2 z \left (t \right )] \]

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

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

\[ {}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ] \]

\[ {}\left [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \frac {3 x \left (t \right )}{4}-\frac {3 y \left (t \right )}{2}+3 z \left (t \right ), z^{\prime }\left (t \right ) = \frac {x \left (t \right )}{8}+\frac {y \left (t \right )}{4}-\frac {z \left (t \right )}{2}\right ] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )-2 z \left (t \right ), z^{\prime }\left (t \right ) = 6 z \left (t \right )] \]

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

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

\[ {}\left [x^{\prime }\left (t \right ) = \frac {9 x \left (t \right )}{10}+\frac {21 y \left (t \right )}{10}+\frac {16 z \left (t \right )}{5}, y^{\prime }\left (t \right ) = \frac {7 x \left (t \right )}{10}+\frac {13 y \left (t \right )}{2}+\frac {21 z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {11 x \left (t \right )}{10}+\frac {17 y \left (t \right )}{10}+\frac {17 z \left (t \right )}{5}\right ] \]

\[ {}\left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )-\frac {9 x_{4} \left (t \right )}{5}, x_{2}^{\prime }\left (t \right ) = \frac {51 x_{2} \left (t \right )}{10}-x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )-\frac {31 x_{3} \left (t \right )}{10}+4 x_{4} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -\frac {14 x_{1} \left (t \right )}{5}+\frac {3 x_{4} \left (t \right )}{2}-x_{5} \left (t \right )\right ] \]

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -6 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+4 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+5 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 12 x \left (t \right )-9 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right )] \]

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+6 y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-8 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-12 y \left (t \right )-14 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-2 z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-7, y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )+5] \]

\[ {}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+9 y \left (t \right )+2, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+6] \]

\[ {}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+5 y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )+10, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t}] \]

\[ {}[x^{\prime }\left (t \right ) = 9 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = 6 x \left (t \right )+4 y \left (t \right )+3 z \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+2 t +1, y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+3 t -1] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}\{x^{\prime }\left (t \right )+3 x \left (t \right )+4 y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = 0\} \]

\[ {}\{x^{\prime }\left (t \right ) = -5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-7 y \left (t \right )\} \]

\[ {}\{x^{\prime }\left (t \right ) = a_{1} x \left (t \right )+b_{1} y \left (t \right )+c_{1}, y^{\prime }\left (t \right ) = a_{2} x \left (t \right )+b_{2} y \left (t \right )+c_{2}\} \]

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

\[ {}[x^{\prime }\left (t \right )+y \left (t \right )-t^{2}+6 t +1 = 0, y^{\prime }\left (t \right )-x \left (t \right ) = -3 t^{2}+3 t +1] \]

\[ {}[x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{2 t}, y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = {\mathrm e}^{t}] \]

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

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

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3] \]

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}] \]

\[ {}[4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}] \]

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

\[ {}[x^{\prime }\left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right ) = g \left (t \right ), y^{\prime }\left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right ) = h \left (t \right )] \]

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