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# |
ODE |
Mathematica |
Maple |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 10 y \left (t \right ), y^{\prime }\left (t \right ) = -10 x \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{2}, y^{\prime }\left (t \right ) = -8 x \left (t \right )\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 8 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-7 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 13 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -9 x \left (t \right )+6 y \left (t \right )]
\] |
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\[
{}[10 x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{3} \left (t \right ), 10 x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), 10 x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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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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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+9 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )+2 t, y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-{\mathrm e}^{2 t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )+2 \sin \left (2 t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )-\cos \left (2 t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right ), 2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = 3 x \left (t \right )]
\] |
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\[
{}[-x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}, 3 x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right ) = x \left (t \right )-15 y \left (t \right )+{\mathrm e}^{-t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )-z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right ), z^{\prime }\left (t \right ) = -4 y \left (t \right )+4 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )-t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-{\mathrm e}^{t} y \left (t \right )+\cos \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+t^{2} y \left (t \right )-\sin \left (t \right )]
\] |
✗ |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 5 y \left (t \right )-7 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )+z \left (t \right )+t, y^{\prime }\left (t \right ) = x \left (t \right )-3 z \left (t \right )+t^{2}, z^{\prime }\left (t \right ) = 6 y \left (t \right )-7 z \left (t \right )+t^{3}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = t x \left (t \right )-y \left (t \right )+{\mathrm e}^{t} z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+t^{2} y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{-t} x \left (t \right )+3 t y \left (t \right )+t^{3} z \left (t \right )]
\] |
✗ |
✗ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right )+x_{4} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2}, x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3}]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-11 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+9 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-6 x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-12 x_{2} \left (t \right )-x_{3} \left (t \right )-6 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )-x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -50 x_{1} \left (t \right )+20 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 100 x_{1} \left (t \right )-60 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+7 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+7 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+5 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-6 x_{2} \left (t \right )-5 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+9 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-10 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+8 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -21 x_{1} \left (t \right )-5 x_{2} \left (t \right )-27 x_{3} \left (t \right )-9 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -21 x_{3} \left (t \right )-2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+7 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+10 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+10 x_{2} \left (t \right )+4 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )+3 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right )-t^{2}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right )+x_{4} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{4} \left (t \right )+t^{2}, x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+t^{3}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -50 x_{1} \left (t \right )+20 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 100 x_{1} \left (t \right )-60 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|