| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\csc \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sec \left (t \right )]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2}\right ]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{-t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 t]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {5 x_{2} \left (t \right )}{2}\right ]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {9 x_{1} \left (t \right )}{5}-x_{2} \left (t \right )\right ]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-2, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-2, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+1]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )-1, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+5]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = -\frac {5 y_{1} \left (t \right )}{4}+\frac {3 y_{2} \left (t \right )}{4}, y_{2}^{\prime }\left (t \right ) = \frac {3 y_{1} \left (t \right )}{4}-\frac {5 y_{2} \left (t \right )}{4}\right ]
\]
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = -\frac {4 y_{1} \left (t \right )}{5}+\frac {3 y_{2} \left (t \right )}{5}, y_{2}^{\prime }\left (t \right ) = -\frac {2 y_{1} \left (t \right )}{5}-\frac {11 y_{2} \left (t \right )}{5}\right ]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -8 y_{1} \left (t \right )-4 y_{2} \left (t \right )-6 y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 12 y_{1} \left (t \right )-4 y_{2} \left (t \right )+10 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+y_{2} \left (t \right )-7 y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-3 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )-6 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+6 y_{2} \left (t \right )+2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-2 y_{2} \left (t \right )+2 y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+2 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+7 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -10 y_{1} \left (t \right )+10 y_{2} \left (t \right )-5 y_{3} \left (t \right )]
\]
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+5 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right )]
\]
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✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+7 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-11 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )+12 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-8 y_{2} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -10 y_{1} \left (t \right )+9 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+2 y_{2} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -13 y_{1} \left (t \right )+16 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )+11 y_{2} \left (t \right )]
\]
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✓ |
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 4 y_{2} \left (t \right )+2 y_{3} \left (t \right )]
\]
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✓ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3}-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -\frac {4 y_{1} \left (t \right )}{3}-\frac {4 y_{2} \left (t \right )}{3}+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -\frac {2 y_{1} \left (t \right )}{3}+\frac {y_{2} \left (t \right )}{3}\right ]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-2 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 6 y_{1} \left (t \right )-5 y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -11 y_{1} \left (t \right )+8 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-3 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 15 y_{1} \left (t \right )-9 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 16 y_{1} \left (t \right )-9 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-7 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+24 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )+17 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
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✓ |
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )-y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+2 y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )-4 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -9 y_{1} \left (t \right )-5 y_{2} \left (t \right )+6 y_{3} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-4 y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )+6 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-8 y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right )+9 y_{3} \left (t \right )]
\]
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✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -5 y_{1} \left (t \right )-y_{2} \left (t \right )+11 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -7 y_{1} \left (t \right )+y_{2} \left (t \right )+13 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+8 y_{3} \left (t \right )]
\]
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✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+9 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+4 y_{3} \left (t \right )]
\]
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|
| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+10 y_{2} \left (t \right )-12 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+2 y_{2} \left (t \right )+3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+6 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -6 y_{1} \left (t \right )-4 y_{2} \left (t \right )-4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )-2 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+5 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )-12 y_{2} \left (t \right )+10 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+11 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )-24 y_{2} \left (t \right )+8 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-12 y_{2} \left (t \right )+8 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-9 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-6 y_{2} \left (t \right )+y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-3 y_{2} \left (t \right )-y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )-2 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+4 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )+5 y_{2} \left (t \right )-8 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+3 y_{2} \left (t \right )-5 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-y_{2} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -y_{1} \left (t \right )-y_{2} \left (t \right )-2 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -5 y_{1} \left (t \right )+5 y_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -11 y_{1} \left (t \right )+4 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -26 y_{1} \left (t \right )+9 y_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+2 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+5 y_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-6 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 3 y_{1} \left (t \right )-y_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )-3 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{2} \left (t \right )+2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )+y_{2} \left (t \right )+y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+3 y_{2} \left (t \right )+y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )-5 y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+7 y_{2} \left (t \right )+3 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = y_{2} \left (t \right )+y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y_{1}^{\prime }\left (t \right ) = -3 y_{1} \left (t \right )+y_{2} \left (t \right )-3 y_{3} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-y_{2} \left (t \right )+2 y_{3} \left (t \right ), y_{3}^{\prime }\left (t \right ) = 4 y_{1} \left (t \right )-2 y_{2} \left (t \right )+3 y_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+t, y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )-1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )+\sin \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+\tan \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+\textit {f\_1} \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+f_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -10 x_{1} \left (t \right )+4 x_{2} \left (t \right )-12 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+2 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+6 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+9 x_{3} \left (t \right )+18 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+10 x_{2} \left (t \right )+15 x_{3} \left (t \right )+30 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+14 x_{2} \left (t \right )+21 x_{3} \left (t \right )+42 x_{4} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|