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# |
ODE |
Mathematica |
Maple |
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\[
{}y^{\prime \prime \prime }+9 y^{\prime \prime }+24 y^{\prime }+16 y = 8 \,{\mathrm e}^{-x}+1
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime }-4 y = 5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
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✓ |
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\[
{}y^{\prime \prime }-y = 4 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+x y = \sin \left (x \right )
\] |
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\[
{}y^{\prime \prime }+4 y = \ln \left (x \right )
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }-3 y = 5 \,{\mathrm e}^{x}
\] |
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\[
{}y^{\prime \prime }+y = \tan \left (x \right )
\] |
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\[
{}y^{\prime \prime }+y = 4 \cos \left (2 x \right )+3 \,{\mathrm e}^{x}
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+5 \,{\mathrm e}^{4 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+t, x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+1]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right )+5 \,{\mathrm e}^{2 t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -\tan \left (t \right ) x_{1} \left (t \right )+3 \cos \left (t \right )^{2}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+\tan \left (t \right ) x_{2} \left (t \right )+2 \sin \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -b x_{1} \left (t \right )-a x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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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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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t}, x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{t}+t x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{t}\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+5 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )+4 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+5 x_{2} \left (t \right )+6 x_{3} \left (t \right )+7 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 7 x_{1} \left (t \right )+6 x_{2} \left (t \right )+5 x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-6 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -b x_{1} \left (t \right )-a x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 15 x_{1} \left (t \right )-32 x_{2} \left (t \right )+12 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-17 x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )+2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-3 x_{2} \left (t \right )+{\mathrm e}^{2 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+t \,{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+{\mathrm e}^{3 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+20 \,{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )+12 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+54 t \,{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+9 \,{\mathrm e}^{3 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+8 \sin \left (2 t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )+8 \cos \left (2 t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-3 \,{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+6 t \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+2 x_{3} \left (t \right )+6 \,{\mathrm e}^{-t}, x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )+{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )+2 x_{3} \left (t \right )-{\mathrm e}^{3 t}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right )-x_{3} \left (t \right )+4 \,{\mathrm e}^{3 t}, x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )+3 \,{\mathrm e}^{3 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )+34 \sin \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-2 x_{2} \left (t \right )+17 \cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{2} \left (t \right )-8 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )-7 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+6 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -12 x_{1} \left (t \right )+10 x_{2} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{2} \left (t \right )-7 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right )-x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -4 x_{2} \left (t \right )+9 x_{3} \left (t \right )-3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = \left (2 t -1\right ) x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = {\mathrm e}^{-t^{2}+t} x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-\cos \left (t \right ) t\right ]
\] |
✗ |
✗ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 9 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 10 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )+2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-5 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-7 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+6 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+13 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-10 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+11 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|