\[ {}y^{\prime \prime \prime }+27 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-6 y = 0 \]

\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \]

\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \]

\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+100 y^{\prime }-500 y = 0 \]

\[ {}y^{\prime \prime \prime } = y \]

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

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+4 x y^{\prime } = 0 \]

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

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

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

\[ {}x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 x y^{\prime }+y = 0 \]

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )] \]

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

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )] \]

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = -50 x_{1} \left (t \right )+20 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 100 x_{1} \left (t \right )-60 x_{2} \left (t \right )] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+9 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+8 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -21 x_{3} \left (t \right )-2 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -40 x_{1} \left (t \right )-12 x_{2} \left (t \right )+54 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 35 x_{1} \left (t \right )+13 x_{2} \left (t \right )-46 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -25 x_{1} \left (t \right )-7 x_{2} \left (t \right )+34 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -20 x_{1} \left (t \right )+11 x_{2} \left (t \right )+13 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 12 x_{1} \left (t \right )-x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -48 x_{1} \left (t \right )+21 x_{2} \left (t \right )+31 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 147 x_{1} \left (t \right )+23 x_{2} \left (t \right )-202 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -90 x_{1} \left (t \right )-9 x_{2} \left (t \right )+129 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 90 x_{1} \left (t \right )+15 x_{2} \left (t \right )-123 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-7 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -12 x_{1} \left (t \right )+7 x_{2} \left (t \right )+11 x_{3} \left (t \right )+9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 24 x_{1} \left (t \right )-17 x_{2} \left (t \right )-19 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -18 x_{1} \left (t \right )+13 x_{2} \left (t \right )+17 x_{3} \left (t \right )+9 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 13 x_{1} \left (t \right )-42 x_{2} \left (t \right )+106 x_{3} \left (t \right )+139 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-16 x_{2} \left (t \right )+52 x_{3} \left (t \right )+70 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )-20 x_{3} \left (t \right )-31 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-6 x_{2} \left (t \right )+22 x_{3} \left (t \right )+33 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 23 x_{1} \left (t \right )-18 x_{2} \left (t \right )-16 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+7 x_{3} \left (t \right )+9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 34 x_{1} \left (t \right )-27 x_{2} \left (t \right )-26 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -26 x_{1} \left (t \right )+21 x_{2} \left (t \right )+25 x_{3} \left (t \right )+12 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 47 x_{1} \left (t \right )-8 x_{2} \left (t \right )+5 x_{3} \left (t \right )-5 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+32 x_{2} \left (t \right )+18 x_{3} \left (t \right )-2 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 139 x_{1} \left (t \right )-40 x_{2} \left (t \right )-167 x_{3} \left (t \right )-121 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -232 x_{1} \left (t \right )+64 x_{2} \left (t \right )+360 x_{3} \left (t \right )+248 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 139 x_{1} \left (t \right )-14 x_{2} \left (t \right )-52 x_{3} \left (t \right )-14 x_{4} \left (t \right )+28 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -22 x_{1} \left (t \right )+5 x_{2} \left (t \right )+7 x_{3} \left (t \right )+8 x_{4} \left (t \right )-7 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 370 x_{1} \left (t \right )-38 x_{2} \left (t \right )-139 x_{3} \left (t \right )-38 x_{4} \left (t \right )+76 x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 152 x_{1} \left (t \right )-16 x_{2} \left (t \right )-59 x_{3} \left (t \right )-13 x_{4} \left (t \right )+35 x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = 95 x_{1} \left (t \right )-10 x_{2} \left (t \right )-38 x_{3} \left (t \right )-7 x_{4} \left (t \right )+23 x_{5} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+13 x_{2} \left (t \right )-13 x_{6} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -14 x_{1} \left (t \right )+19 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )+4 x_{6} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -30 x_{1} \left (t \right )+12 x_{2} \left (t \right )-7 x_{3} \left (t \right )-30 x_{4} \left (t \right )+12 x_{5} \left (t \right )+18 x_{6} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-10 x_{3} \left (t \right )-9 x_{4} \left (t \right )+10 x_{5} \left (t \right )+2 x_{6} \left (t \right ), x_{5}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+6 x_{4} \left (t \right )+5 x_{5} \left (t \right )-15 x_{6} \left (t \right ), x_{6}^{\prime }\left (t \right ) = -14 x_{1} \left (t \right )+23 x_{2} \left (t \right )-10 x_{3} \left (t \right )-20 x_{4} \left (t \right )+10 x_{5} \left (t \right )] \]

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

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

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

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

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

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = 25 x_{1} \left (t \right )+12 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -18 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+13 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -19 x_{1} \left (t \right )+12 x_{2} \left (t \right )+84 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+4 x_{2} \left (t \right )+33 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -13 x_{1} \left (t \right )+40 x_{2} \left (t \right )-48 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+23 x_{2} \left (t \right )-24 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )] \]

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

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

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 18 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -27 x_{1} \left (t \right )-9 x_{2} \left (t \right )-5 x_{3} \left (t \right )] \]

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

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

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

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

\[ {}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+7 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -6 x_{2} \left (t \right )-14 x_{3} \left (t \right )+x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 39 x_{1} \left (t \right )+8 x_{2} \left (t \right )-16 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -36 x_{1} \left (t \right )-5 x_{2} \left (t \right )+16 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 72 x_{1} \left (t \right )+16 x_{2} \left (t \right )-29 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 28 x_{1} \left (t \right )+50 x_{2} \left (t \right )+100 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 15 x_{1} \left (t \right )+33 x_{2} \left (t \right )+60 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -15 x_{1} \left (t \right )-30 x_{2} \left (t \right )-57 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+17 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+2 x_{3} \left (t \right )] \]

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

\[ {}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+5 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-8 x_{2} \left (t \right )+10 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -15 x_{1} \left (t \right )-7 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 34 x_{1} \left (t \right )+16 x_{2} \left (t \right )-11 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 17 x_{1} \left (t \right )+7 x_{2} \left (t \right )+5 x_{3} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-4 x_{2} \left (t \right )-6 x_{3} \left (t \right )+11 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )+6 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )-5 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -13 x_{2} \left (t \right )+22 x_{3} \left (t \right )-12 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -27 x_{2} \left (t \right )+45 x_{3} \left (t \right )-25 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 35 x_{1} \left (t \right )-12 x_{2} \left (t \right )+4 x_{3} \left (t \right )+30 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 22 x_{1} \left (t \right )-8 x_{2} \left (t \right )+3 x_{3} \left (t \right )+19 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+3 x_{2} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -27 x_{1} \left (t \right )+9 x_{2} \left (t \right )-3 x_{3} \left (t \right )-23 x_{4} \left (t \right )] \]

\[ {}[x_{1}^{\prime }\left (t \right ) = 11 x_{1} \left (t \right )-x_{2} \left (t \right )+26 x_{3} \left (t \right )+6 x_{4} \left (t \right )-3 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-24 x_{3} \left (t \right )-6 x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+9 x_{3} \left (t \right )+5 x_{4} \left (t \right )-x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -48 x_{1} \left (t \right )-3 x_{2} \left (t \right )-138 x_{3} \left (t \right )-30 x_{4} \left (t \right )+18 x_{5} \left (t \right )] \]

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

\[ {}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-8 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -18 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-3 x_{2} \left (t \right )-25 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 33 x_{1} \left (t \right )+10 x_{2} \left (t \right )+90 x_{3} \left (t \right )+32 x_{4} \left (t \right )] \]

\[ {}y^{\prime } = y \]

\[ {}y^{\prime } = 4 y \]

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

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

\[ {}y^{\prime } = x^{2} y \]

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

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

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

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