| # | ODE | Mathematica | Maple | Sympy |
| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 a x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \left (a^{2}+9\right ) x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-5 y \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = a x_{1} \left (t \right )+5 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = a x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = a x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+a x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{4} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -a x_{3} \left (t \right )-b x_{2} \left (t \right )-c x_{1} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -2 y \left (t \right )-x \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{3}, y^{\prime }\left (t \right ) = -y \left (t \right )^{3}]
\]
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| \[
{} [2 x^{\prime }\left (t \right )-3 x \left (t \right )-2 y^{\prime }\left (t \right ) = t, 2 x^{\prime }\left (t \right )+3 x \left (t \right )+2 y^{\prime }\left (t \right )+8 y \left (t \right ) = 2]
\]
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| \[
{} [y^{\prime }\left (t \right ) = 2 y \left (t \right )-5 z \left (t \right ), z^{\prime }\left (t \right ) = 4 y \left (t \right )-2 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )-6 x \left (t \right )+3 y \left (t \right ) = 8 \,{\mathrm e}^{t}, y^{\prime }\left (t \right )-2 x \left (t \right )-y \left (t \right ) = 4 \,{\mathrm e}^{t}]
\]
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| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )+4 y \left (t \right ) = 0]
\]
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| \[
{} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1]
\]
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| \[
{} \left [y^{\prime }\left (t \right ) = -\sqrt {1-y \left (t \right )^{2}}, x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )\right ]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+12 y \left (t \right )]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-y \left (t \right )+6 z \left (t \right ), y^{\prime }\left (t \right ) = -10 x \left (t \right )+4 y \left (t \right )-12 z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x \left (t \right )+y^{\prime }\left (t \right ) = \sin \left (t \right )+\cos \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )-\sin \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )+y \left (t \right )]
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = 6 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\]
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| \[
{} [2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = 2 \,{\mathrm e}^{2 t}, x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = 0]
\]
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| \[
{} [y^{\prime }\left (t \right ) = y \left (t \right )-3 z \left (t \right ), z^{\prime }\left (t \right ) = 2 y \left (t \right )-4 z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )-y \left (t \right )+6 z \left (t \right ), y^{\prime }\left (t \right ) = -10 x \left (t \right )+4 y \left (t \right )-12 z \left (t \right ), z^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = 3 x \left (t \right )+3 y \left (t \right )-z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = 3 y \left (t \right )+z \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )+1]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )-5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right )-4]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )+3 \,{\mathrm e}^{2 t}, y^{\prime }\left (t \right ) = -4 x \left (t \right )+2 y \left (t \right )+t \,{\mathrm e}^{2 t}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )-7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-8 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+6 y \left (t \right )]
\]
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✓ |
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right )+2 x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = \sin \left (2 x \left (t \right )\right )-5 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 8 x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = 6 x \left (t \right )^{2}-6 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{2}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{3}-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )^{2}-x \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )^{2}-x \left (t \right ) y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = 0, x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-y \left (t \right ) = t]
\]
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| \[
{} [y^{\prime }\left (t \right )-3 z \left (t \right ) = 5, y \left (t \right )-z^{\prime }\left (t \right )-x \left (t \right ) = 3-2 t, z \left (t \right )+x^{\prime }\left (t \right ) = -1]
\]
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✓ |
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✓ |
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| \[
{} [x^{\prime \prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+x \left (t \right )-y^{\prime }\left (t \right )-y \left (t \right ) = 3 \,{\mathrm e}^{t}]
\]
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✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )-2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = 1, y^{\prime }\left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 2, 3 x \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 3]
\]
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✓ |
✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right ) = 0, y^{\prime }\left (t \right )+y \left (t \right )-3 x \left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [x^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 y \left (t \right )-3 x \left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y^{\prime }\left (t \right )+y \left (t \right )-x^{\prime \prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{-t}]
\]
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✓ |
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| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 0, y^{\prime }\left (t \right )+2 y \left (t \right )+z^{\prime }\left (t \right )+2 z \left (t \right ) = 2, x \left (t \right )+z^{\prime }\left (t \right )-z \left (t \right ) = 0]
\]
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| \[
{} [x^{\prime \prime }\left (t \right ) = 1, x^{\prime }\left (t \right )+x \left (t \right )+y^{\prime \prime }\left (t \right )-9 y \left (t \right )+z^{\prime }\left (t \right )+z \left (t \right ) = 0, 5 x \left (t \right )+z^{\prime \prime }\left (t \right )-4 z \left (t \right ) = 2]
\]
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✓ |
✓ |
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| \[
{} [y^{\prime }\left (t \right )-3 z \left (t \right ) = 5, y \left (t \right )-z^{\prime }\left (t \right )-x \left (t \right ) = 3-2 t, z \left (t \right )+x^{\prime }\left (t \right ) = -1]
\]
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✓ |
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✓ |
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| \[
{} [y^{\prime }\left (t \right )+y \left (t \right )-x^{\prime }\left (t \right )+x \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )+4 y \left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [w^{\prime }\left (t \right )+y \left (t \right ) = \sin \left (t \right ), y^{\prime }\left (t \right )-z \left (t \right ) = {\mathrm e}^{t}, w \left (t \right )+y \left (t \right )+z^{\prime }\left (t \right ) = 1]
\]
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| \[
{} [y^{\prime \prime }\left (t \right )+z \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )+z^{\prime }\left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [z^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right ) = \cos \left (t \right ), y^{\prime \prime }\left (t \right )-z \left (t \right ) = \sin \left (t \right )]
\]
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✓ |
✓ |
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| \[
{} [w^{\prime \prime }\left (t \right )-y \left (t \right )+2 z \left (t \right ) = 3 \,{\mathrm e}^{-t}, -2 w^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+z \left (t \right ) = 0, 2 w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime }\left (t \right )+2 z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [y^{\prime }\left (t \right )+z \left (t \right ) = t, z^{\prime }\left (t \right )-y \left (t \right ) = 0]
\]
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✓ |
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✓ |
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| \[
{} [y^{\prime }\left (t \right )-z \left (t \right ) = 0, y \left (t \right )-z^{\prime }\left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
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| \[
{} [w^{\prime }\left (t \right )-w \left (t \right )-2 y \left (t \right ) = 1, y^{\prime }\left (t \right )-4 w \left (t \right )-3 y \left (t \right ) = -1]
\]
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| \[
{} [w^{\prime }\left (t \right )-y \left (t \right ) = 0, w \left (t \right )+y^{\prime }\left (t \right )+z \left (t \right ) = 1, w \left (t \right )-y \left (t \right )+z^{\prime }\left (t \right ) = 2 \sin \left (t \right )]
\]
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| \[
{} [u^{\prime \prime }\left (t \right )-2 v \left (t \right ) = 2, u \left (t \right )+v^{\prime }\left (t \right ) = 5 \,{\mathrm e}^{2 t}+1]
\]
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| \[
{} [w^{\prime \prime }\left (t \right )-2 z \left (t \right ) = 0, w^{\prime }\left (t \right )+y^{\prime }\left (t \right )-z \left (t \right ) = 2 t, w^{\prime }\left (t \right )-2 y \left (t \right )+z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [w^{\prime \prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = -1, w \left (t \right )+y^{\prime \prime }\left (t \right )-z \left (t \right ) = 0, -w \left (t \right )-y^{\prime }\left (t \right )+z^{\prime \prime }\left (t \right ) = 0]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{t}]
\]
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✓ |
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| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+3]
\]
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|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+6 y \left (t \right )+t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )-5 z \left (t \right )+3, z^{\prime }\left (t \right ) = y \left (t \right )+2 z \left (t \right )]
\]
|
✗ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 \,{\mathrm e}^{-t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (t \right ) = x \left (t \right ), x^{\prime }\left (t \right ) = -y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [u^{\prime }\left (x \right ) = 2 v \left (x \right )-1, v^{\prime }\left (x \right ) = 1+2 u \left (x \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime \prime }\left (t \right ) = x \left (t \right ), y^{\prime \prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime \prime }\left (t \right ) = x \left (t \right )-2, y^{\prime \prime }\left (t \right ) = y \left (t \right )+2]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [y^{\prime }\left (t \right )+6 y \left (t \right ) = x^{\prime }\left (t \right ), 3 x \left (t \right )-x^{\prime }\left (t \right ) = 2 y^{\prime }\left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right ) = 1, 2 x \left (t \right )+y^{\prime }\left (t \right )-2 y \left (t \right ) = t]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = -\sin \left (t \right ), x^{\prime }\left (t \right )-3 x \left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = 4 \cos \left (t \right )]
\]
|
✓ |
✓ |
✗ |
|
| \[
{} [x^{\prime \prime }\left (t \right )+2 y^{\prime }\left (t \right )+8 x \left (t \right ) = 32 t, y^{\prime \prime }\left (t \right )+3 x^{\prime }\left (t \right )-2 y \left (t \right ) = 60 \,{\mathrm e}^{-t}]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} \left [x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = \sqrt {t}\right ]
\]
|
✓ |
✓ |
✓ |
|
| \[
{} [x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right ), 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = \sin \left (t \right )]
\]
|
✗ |
✓ |
✗ |
|
| \[
{} [r^{\prime \prime }\left (t \right ) = r \left (t \right )+y \left (t \right ), y^{\prime \prime }\left (t \right ) = 5 r \left (t \right )-3 y \left (t \right )+t^{2}]
\]
|
✓ |
✗ |
✓ |
|
| \[
{} [x \left (t \right ) y^{\prime }\left (t \right )+y \left (t \right ) x^{\prime }\left (t \right ) = t^{2}, 2 x^{\prime \prime }\left (t \right )-y^{\prime }\left (t \right ) = 5 t]
\]
|
✗ |
✗ |
✗ |
|
| \[
{} [x^{\prime \prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = y \left (t \right )+\sin \left (t \right ), y^{\prime \prime }\left (t \right )+x^{\prime }\left (t \right )-y \left (t \right ) = 2 t^{2}-x \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|