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

\[ {}[y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+2 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+7 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -10 y_{1} \left (t \right )+10 y_{2} \left (t \right )-5 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+7 y_{2} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-11 y_{2} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )+12 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-8 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -10 y_{1} \left (t \right )+9 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+2 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -13 y_{1} \left (t \right )+16 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )+11 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 4 y_{2} \left (t \right )+2 y_{3} \left (t \right )] \]

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

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

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

\[ {}[y_{1}^{\prime }\left (t \right ) = 6 y_{1} \left (t \right )-5 y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -11 y_{1} \left (t \right )+8 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-3 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 15 y_{1} \left (t \right )-9 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 16 y_{1} \left (t \right )-9 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-7 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+24 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+17 y_{2} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-y_{2} \left (t \right )] \]

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

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )-4 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )-5 y_{2} \left (t \right )+6 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-8 y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+9 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -5 y_{1} \left (t \right )-y_{2} \left (t \right )+11 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+y_{2} \left (t \right )+13 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+8 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+9 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+10 y_{2} \left (t \right )-12 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+6 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-12 y_{2} \left (t \right )+10 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+11 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+8 y_{3} \left (t \right )] \]

\[ {}[y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-12 y_{2} \left (t \right )+8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-9 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-6 y_{2} \left (t \right )+y_{3} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )+5 y_{2} \left (t \right )-8 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-5 y_{3} \left (t \right )] \]

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

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -11 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -26 y_{1} \left (t \right )+9 y_{2} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-6 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-y_{2} \left (t \right )] \]

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

\[ {}[y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-5 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+7 y_{2} \left (t \right )+3 y_{3} \left (t \right )] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} y+y^{\prime } = 1 \]

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

\[ {}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1} \]

\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \]

\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \]

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

\[ {}t y+y^{\prime } = t +1 \]

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

\[ {}y^{\prime }-2 t y = 1 \]

\[ {}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{\frac {5}{2}} \]

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

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

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

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

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

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

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

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

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

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

\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \]

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

\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \]

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

\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \]

\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \]

\[ {}3 t y^{\prime } = \cos \left (t \right ) y \]

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

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

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

\[ {}y^{\prime } = \frac {t +y}{t -y} \]

\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \]

\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \]

\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \]

\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \]

\[ {}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \]

\[ {}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0 \]

\[ {}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0 \]

\[ {}\frac {y^{2}}{2}-2 \,{\mathrm e}^{t} y+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \]

\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \]

\[ {}2 t \cos \left (y\right )+3 t^{2} y+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime } = 0 \]

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

\[ {}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0 \]

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

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

\[ {}y^{\prime } = 1+y+y^{2} \cos \left (t \right ) \]

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

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