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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = 0] \]

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

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

\[ {}\left [x^{\prime }\left (t \right ) = -10 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = 28 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -\frac {8 z \left (t \right )}{3}\right ] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )] \]

\[ {}\left [x^{\prime }\left (t \right ) = \pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5}, y^{\prime }\left (t \right ) = \sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000}\right ] \]

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

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

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

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )] \]

\[ {}[t x^{\prime }\left (t \right )+2 x \left (t \right ) = 15 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )] \]

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

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

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

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

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

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

\[ {}[x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )] \]

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

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )-17, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-13] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+24 t] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right )] \]

\[ {}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right )] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 1] \]

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

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

\[ {}[x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )] \]

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

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

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

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

\[ {}\left [x_{1}^{\prime }\left (t \right ) = -2 t x_{1} \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )+t}{t}\right ] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = {\mathrm e}^{t -x_{1} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{x_{1} \left (t \right )}] \]

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

\[ {}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )^{2}}{x_{2} \left (t \right )}, x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{1} \left (t \right )\right ] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}\left [{\mathrm e}^{t} x^{\prime }\left (t \right ) = \frac {1}{y \left (t \right )}, {\mathrm e}^{t} y^{\prime }\left (t \right ) = \frac {1}{x \left (t \right )}\right ] \]

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

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