| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime \prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = 0, x \left (t \right )+y^{\prime \prime }\left (t \right )+y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+2 y \left (t \right ) = 3 \,{\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = 4 \,{\mathrm e}^{2 t}]
\]
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| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+2 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+x \left (t \right )+24 y \left (t \right ) = 3]
\]
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| \[
{} [x^{\prime }\left (t \right )+4 x \left (t \right )+3 y \left (t \right ) = t, y^{\prime }\left (t \right )+2 x \left (t \right )+5 y \left (t \right ) = {\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = n y \left (t \right )-m z \left (t \right ), y^{\prime }\left (t \right ) = L z \left (t \right )-m x \left (t \right ), z^{\prime }\left (t \right ) = m x \left (t \right )-L y \left (t \right )]
\]
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| \[
{} [t x^{\prime }\left (t \right )+y \left (t \right ) = 0, t y^{\prime }\left (t \right )+x \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
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| \[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+11 x \left (t \right )+31 y \left (t \right ) = {\mathrm e}^{t}, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+8 x \left (t \right )+24 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
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| \[
{} [t x^{\prime }\left (t \right ) = t -2 x \left (t \right ), t y^{\prime }\left (t \right ) = t x \left (t \right )+t y \left (t \right )+2 x \left (t \right )-t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )+2 \sin \left (2 t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )+2 \,{\mathrm e}^{-3 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 \cos \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+3 \sin \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 12 x \left (t \right )-15 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-13 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 16 x \left (t \right )+8 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )+2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right )+1, y^{\prime }\left (t \right ) = -6 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right )+\sin \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \cos \left (t \right ) x \left (t \right )-\sin \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) \sin \left (t \right )+\cos \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \left (3 t -1\right ) x \left (t \right )-\left (1-t \right ) y \left (t \right )+t \,{\mathrm e}^{t^{2}}, y^{\prime }\left (t \right ) = -\left (t +2\right ) x \left (t \right )+\left (t -2\right ) y \left (t \right )-{\mathrm e}^{t^{2}}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} \left [w_{1}^{\prime }\left (z \right ) = w_{2} \left (z \right ), w_{2}^{\prime }\left (z \right ) = \frac {a w_{1} \left (z \right )}{z^{2}}\right ]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = a y \left (t \right ), y^{\prime }\left (t \right ) = -a x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right ), y^{\prime }\left (t \right ) = a y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = a y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+t, y^{\prime }\left (t \right ) = -y \left (t \right )+2 t]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+2 t, y^{\prime }\left (t \right ) = 3 y \left (t \right )+t^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+2 t, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+t^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )-{\mathrm e}^{t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )+2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+3 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right ), z^{\prime }\left (t \right ) = 4 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \left (a -2\right ) x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\left (a -2\right ) y \left (t \right ), z^{\prime }\left (t \right ) = -a z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )+t y \left (t \right ) = -1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = 2]
\]
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| \[
{} [x^{\prime }\left (t \right )+y \left (t \right ) = 3 t, y^{\prime }\left (t \right )-t x^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-t y \left (t \right ) = 1, y^{\prime }\left (t \right )-t x^{\prime }\left (t \right ) = 3]
\]
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| \[
{} [t^{2} x^{\prime }\left (t \right )-y \left (t \right ) = 1, y^{\prime }\left (t \right )-2 x \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right )-y \left (t \right ) = 3, y^{\prime }\left (t \right )-3 x^{\prime }\left (t \right ) = -2 x \left (t \right )]
\]
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| \[
{} [t x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = 1, y^{\prime }\left (t \right )+x \left (t \right )+{\mathrm e}^{x^{\prime }\left (t \right )} = 1]
\]
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| \[
{} [x \left (t \right ) x^{\prime }\left (t \right )+y \left (t \right ) = 2 t, y^{\prime }\left (t \right )+2 x \left (t \right )^{2} = 1]
\]
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|
| \[
{} [x^{\prime }\left (t \right ) = 1+x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-1]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+a, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+b]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = a x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+b y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 c x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 x \left (t \right ) y \left (t \right )-a x \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+4 x \left (t \right ) y \left (t \right )-a y \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-4 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+x \left (t \right ) y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) \left (3-y \left (t \right )\right ), y^{\prime }\left (t \right ) = y \left (t \right ) \left (x \left (t \right )-5\right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+\delta \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|