| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [y_{1}^{\prime }\left (t \right ) = y_{2} \left (t \right )+y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{2}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right )-y_{3} \left (t \right )+{\mathrm e}^{2 t}, y_{3}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right )+3 y_{3} \left (t \right )-{\mathrm e}^{2 t}]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = -2 y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -4 y_{1} \left (t \right )+3 y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 5 y_{1} \left (t \right )-3 y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = 2 y_{1} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -y_{1} \left (t \right )+\frac {y_{2} \left (t \right )}{t}\right ]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = \left (2 t +1\right ) y_{1} \left (t \right )+2 t y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -2 t y_{1} \left (t \right )+\left (1-2 t \right ) y_{2} \left (t \right )]
\]
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✓ |
✓ |
✓ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = y_{1} \left (t \right )+y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {y_{2} \left (t \right )}{t}\right ]
\]
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✓ |
✓ |
✓ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{2} \left (t \right )}{t}+t\right ]
\]
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✓ |
✓ |
✗ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = -\frac {y_{2} \left (t \right )}{t}+1, y_{2}^{\prime }\left (t \right ) = \frac {y_{1} \left (t \right )}{t}+\frac {2 y_{2} \left (t \right )}{t}-1\right ]
\]
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✓ |
✓ |
✗ |
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| \[
{} \left [y_{1}^{\prime }\left (t \right ) = \frac {4 t y_{1} \left (t \right )}{t^{2}+1}+\frac {6 y_{2} \left (t \right ) t}{t^{2}+1}-3 t, y_{2}^{\prime }\left (t \right ) = -\frac {2 t y_{1} \left (t \right )}{t^{2}+1}-\frac {4 y_{2} \left (t \right ) t}{t^{2}+1}+t\right ]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = 3 \sec \left (t \right ) y_{1} \left (t \right )+5 \sec \left (t \right ) y_{2} \left (t \right ), y_{2}^{\prime }\left (t \right ) = -\sec \left (t \right ) y_{1} \left (t \right )-3 \sec \left (t \right ) y_{2} \left (t \right )]
\]
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✗ |
✓ |
✓ |
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| \[
{} [y_{1}^{\prime }\left (t \right ) = t y_{1} \left (t \right )+t y_{2} \left (t \right )+4 t, y_{2}^{\prime }\left (t \right ) = -t y_{1} \left (t \right )-t y_{2} \left (t \right )+4 t]
\]
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✓ |
✓ |
✓ |
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