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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}x^{\prime }+3 x = {\mathrm e}^{-2 t} \]

\[ {}x^{\prime }-3 x = 3 t^{3}+3 t^{2}+2 t +1 \]

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

\[ {}2 x^{\prime }+6 x = t \,{\mathrm e}^{-3 t} \]

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

\[ {}x^{\prime \prime } = 0 \]

\[ {}x^{\prime \prime } = 1 \]

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

\[ {}x^{\prime \prime }+x^{\prime } = 0 \]

\[ {}x^{\prime \prime }+x^{\prime } = 0 \]

\[ {}x^{\prime \prime }-x^{\prime } = 1 \]

\[ {}x^{\prime \prime }+x = t \]

\[ {}x^{\prime \prime }+6 x^{\prime } = 12 t +2 \]

\[ {}x^{\prime \prime }-2 x^{\prime }+2 x = 2 \]

\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 4 \]

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

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