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# |
ODE |
Mathematica |
Maple |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{3} \left (t \right )+2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )+9 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+{\mathrm e}^{c t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+f_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+f_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+{\mathrm e}^{3 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-t^{2}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 t]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )-{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )-x_{3} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 \,{\mathrm e}^{2 t}, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-x_{3} \left (t \right )+{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )+x_{3} \left (t \right )-{\mathrm e}^{3 t}, x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )-{\mathrm e}^{3 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{8 t}, x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+2 \,{\mathrm e}^{8 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+3 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 \,{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )-{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+\sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\tan \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+4 \,{\mathrm e}^{t} \cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+f_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+f_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+\delta \left (t -\pi \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+1-\operatorname {Heaviside}\left (t -\pi \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )+{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )+{\mathrm e}^{t} \cos \left (2 t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-2 y \left (t \right )^{2}-3 x \left (t \right ) y \left (t \right )]
\] |
✗ |
✗ |
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\[
{}[x^{\prime }\left (t \right ) = -b x \left (t \right ) y \left (t \right )+m, y^{\prime }\left (t \right ) = b x \left (t \right ) y \left (t \right )-g y \left (t \right )]
\] |
✗ |
✗ |
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\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )-b x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = -c y \left (t \right )+d x \left (t \right ) y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )+x \left (t \right )^{2}+y \left (t \right )^{2}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-x \left (t \right ) y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -y \left (t \right )-y \left (t \right ) x \left (t \right )^{2}, z^{\prime }\left (t \right ) = 1-z \left (t \right )+x \left (t \right )^{2}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )^{2}-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right ) \sin \left (\pi y \left (t \right )\right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = \cos \left (y \left (t \right )\right ), y^{\prime }\left (t \right ) = \sin \left (x \left (t \right )\right )-1]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -1-y \left (t \right )-{\mathrm e}^{x \left (t \right )}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right ) \left ({\mathrm e}^{x \left (t \right )}-1\right ), z^{\prime }\left (t \right ) = x \left (t \right )+\sin \left (z \left (t \right )\right )]
\] |
✗ |
✗ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )^{2}, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right ), z^{\prime }\left (t \right ) = {\mathrm e}^{z \left (t \right )}-x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+z \left (t \right )-2 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )-2 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right )+3 \,{\mathrm e}^{-t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+y \left (t \right )-6 z \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-4 y \left (t \right )+12 z \left (t \right ), z^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ), z^{\prime }\left (t \right ) = 2 h \left (t \right ), h^{\prime }\left (t \right ) = -2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+h \left (t \right ), z^{\prime }\left (t \right ) = 2 h \left (t \right ), h^{\prime }\left (t \right ) = -2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\] |
✗ |
✗ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+5]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\] |
✗ |
✗ |
|
|
\[
{}[x^{\prime }\left (t \right ) = {\mathrm e}^{y \left (t \right )}-x \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{x \left (t \right )}+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-x \left (t \right ) = \cos \left (t \right ), y^{\prime }\left (t \right )+y \left (t \right ) = 4 t]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right ) = 3 t^{2}, y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{3 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+2 x \left (t \right ) = 3 t, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (2 t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 2 \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = 3 y \left (t \right )-3 x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[2 x^{\prime }\left (t \right )+3 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{t}, 5 x \left (t \right )-3 y^{\prime }\left (t \right ) = y \left (t \right )+2 t]
\] |
✓ |
✓ |
|
|
\[
{}[5 y^{\prime }\left (t \right )-3 x^{\prime }\left (t \right )-5 y \left (t \right ) = 5 t, 3 x^{\prime }\left (t \right )-5 y^{\prime }\left (t \right )-2 x \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), z^{\prime }\left (t \right ) = 3 y \left (t \right )-2 z \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|