| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = -5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}, y^{\prime }\left (t \right ) = x \left (t \right )-\frac {y \left (t \right )}{2}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -\frac {9 x \left (t \right )}{10}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\frac {11 y \left (t \right )}{10}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{10}, y^{\prime }\left (t \right ) = \frac {z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {2 x \left (t \right )}{5}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 z \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 5 x \left (t \right )-5 y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = -10 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = 28 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -\frac {8 z \left (t \right )}{3}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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| \[
{} \left [x^{\prime }\left (t \right ) = \pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5}, y^{\prime }\left (t \right ) = \sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000}\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 1-2 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-7 y \left (t \right )]
\]
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| \[
{} [t x^{\prime }\left (t \right )+2 x \left (t \right ) = 15 y \left (t \right ), t y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )-17, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-13]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )+2 y \left (t \right )+7 \,{\mathrm e}^{2 t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-7 \,{\mathrm e}^{2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )-6 \,{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+2 \,{\mathrm e}^{3 t}]
\]
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✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+24 t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+19 \cos \left (4 t \right )-13 \sin \left (4 t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )+5 \operatorname {Heaviside}\left (t -2\right ), y^{\prime }\left (t \right ) = x \left (t \right )+6 y \left (t \right )+17 \operatorname {Heaviside}\left (t -2\right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )+4, y^{\prime }\left (t \right ) = 3 x \left (t \right )-7 y \left (t \right )+5]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-5]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = 4 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|