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

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

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

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

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

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

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

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

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

\[ {}\left [x^{\prime }\left (t \right ) = -\frac {9 x \left (t \right )}{10}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\frac {11 y \left (t \right )}{10}\right ] \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \]

\[ {}y^{\prime \prime }+2 y = 0 \]

\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \]

\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \]

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

\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \]

\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \]

\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \]

\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \]

\[ {}y^{\prime \prime }+2 y = -3 \]

\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+9 y = 6 \]

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

\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \]

\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \]

\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \]

\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \]

\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \]

\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \]

\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \]