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# |
ODE |
Mathematica |
Maple |
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\[
{}t y^{\prime \prime \prime }+\sin \left (t \right ) y^{\prime \prime }+4 y = \cos \left (t \right )
\] |
✗ |
✗ |
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\[
{}t \left (t -1\right ) y^{\prime \prime \prime \prime }+{\mathrm e}^{t} y^{\prime \prime }+7 t^{2} y = 0
\] |
✗ |
✗ |
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\[
{}y^{\prime \prime \prime }+t y^{\prime \prime }+5 t^{2} y^{\prime }+2 t^{3} y = \ln \left (t \right )
\] |
✗ |
✗ |
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\[
{}\left (x -1\right ) y^{\prime \prime \prime \prime }+\left (x +5\right ) y^{\prime \prime }+\tan \left (x \right ) y = 0
\] |
✗ |
✗ |
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\[
{}\left (x^{2}-25\right ) y^{\left (6\right )}+x^{2} y^{\prime \prime }+5 y = 0
\] |
✗ |
✗ |
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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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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime }+y^{\prime } = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime } = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime }+4 y^{\prime \prime }-4 y^{\prime }-16 y = 0
\] |
✓ |
✓ |
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\[
{}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime } = 0
\] |
✓ |
✓ |
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\[
{}x y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
✓ |
✓ |
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\[
{}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+4 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+4 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+6 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+2 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-x_{2} \left (t \right )-\frac {3 x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {3 x_{1} \left (t \right )}{2}-2 x_{2} \left (t \right )-\frac {3 x_{3} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+5 x_{2} \left (t \right )+3 x_{3} \left (t \right )-5 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )+2 x_{3} \left (t \right )-4 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+4 x_{2} \left (t \right )+2 x_{3} \left (t \right )-5 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{3} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{3} \left (t \right )-2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+2 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+8 x_{2} \left (t \right )+5 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+16 x_{2} \left (t \right )+10 x_{3} \left (t \right )+6 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-14 x_{2} \left (t \right )-11 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-8 x_{2} \left (t \right )-5 x_{3} \left (t \right )-3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )+x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )+2 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+x_{2} \left (t \right )-7 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )+2 x_{4} \left (t \right )+3 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{3} \left (t \right )-x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-4 x_{4} \left (t \right )-2 x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right )+2 x_{4} \left (t \right )+x_{5} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{2} \left (t \right )-2 x_{3} \left (t \right )+3 x_{4} \left (t \right )+2 x_{5} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+6 x_{2} \left (t \right )+4 x_{3} \left (t \right )-8 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-8 x_{2} \left (t \right )-6 x_{3} \left (t \right )+8 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )+7 x_{2} \left (t \right )+4 x_{3} \left (t \right )-9 x_{4} \left (t \right )-16 x_{5} \left (t \right ), x_{5}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )+5 x_{4} \left (t \right )+7 x_{5} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+2 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-4 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-3 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = \frac {8 x_{2} \left (t \right )}{3}-2 x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+6 x_{2} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )+5 x_{2} \left (t \right )-9 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {4 x_{1} \left (t \right )}{3}+\frac {4 x_{2} \left (t \right )}{3}-\frac {11 x_{3} \left (t \right )}{3}, x_{2}^{\prime }\left (t \right ) = -\frac {16 x_{1} \left (t \right )}{3}-\frac {x_{2} \left (t \right )}{3}+\frac {14 x_{3} \left (t \right )}{3}, x_{3}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 x_{3} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {3 x_{1} \left (t \right )}{4}+\frac {29 x_{2} \left (t \right )}{4}-\frac {11 x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = -\frac {3 x_{1} \left (t \right )}{4}+\frac {3 x_{2} \left (t \right )}{4}-\frac {5 x_{3} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = \frac {5 x_{1} \left (t \right )}{4}+\frac {11 x_{2} \left (t \right )}{4}-\frac {5 x_{3} \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right )+2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -19 x_{1} \left (t \right )-6 x_{2} \left (t \right )+6 x_{3} \left (t \right )+16 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )+6 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-3 x_{2} \left (t \right )+6 x_{3} \left (t \right )+5 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+6 x_{2} \left (t \right )+2 x_{3} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-3 x_{2} \left (t \right )-6 x_{3} \left (t \right )+2 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+8 x_{2} \left (t \right )+3 x_{3} \left (t \right )-4 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-6 x_{3} \left (t \right )+x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-4 x_{2} \left (t \right )+5 x_{3} \left (t \right )+9 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-5 x_{2} \left (t \right )+4 x_{3} \left (t \right )+12 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{3} \left (t \right )+2 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+2 x_{3} \left (t \right )+3 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-5 x_{2} \left (t \right )+8 x_{3} \left (t \right )+14 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-8 x_{2} \left (t \right )+11 x_{3} \left (t \right )+27 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -6 x_{1} \left (t \right )-4 x_{2} \left (t \right )+7 x_{3} \left (t \right )+17 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+2 x_{3} \left (t \right )+4 x_{4} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )-2 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}+x_{2} \left (t \right )-3 x_{3} \left (t \right )-\frac {5 x_{4} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = 3 x_{2} \left (t \right )-5 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )-3 x_{4} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-3 x_{2} \left (t \right )\right ]
\] |
✓ |
✓ |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{4}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-x_{2} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = -\frac {5 x_{1} \left (t \right )}{2}+2 x_{2} \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+4 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -k_{1} x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = k_{1} x_{1} \left (t \right )-k_{2} x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = k_{2} x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+\sqrt {3}\, x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = \sqrt {3}\, x_{1} \left (t \right )-x_{2} \left (t \right )+\sqrt {3}\, {\mathrm e}^{-t}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )-\cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sin \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{-2 t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 1-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{-t}]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}-\frac {x_{3} \left (t \right )}{2}+1, x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}-\frac {3 x_{3} \left (t \right )}{2}+11 \,{\mathrm e}^{-3 t}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )+3 t, x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+3 \cos \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}+x_{2} \left (t \right )+\frac {x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )-\sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+x_{2} \left (t \right )-\frac {x_{3} \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+9 x_{2} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+11 x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+6 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-16 x_{2} \left (t \right )-16 x_{3} \left (t \right )-17 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-10 x_{2} \left (t \right )-8 x_{3} \left (t \right )-7 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+14 x_{2} \left (t \right )+14 x_{3} \left (t \right )+14 x_{4} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-\frac {3 x_{2} \left (t \right )}{2}-x_{3} \left (t \right )+\frac {7 x_{4} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+\frac {x_{2} \left (t \right )}{2}-\frac {3 x_{4} \left (t \right )}{2}, x_{4}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+\frac {3 x_{2} \left (t \right )}{2}+3 x_{3} \left (t \right )-\frac {7 x_{4} \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -14 x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 15 x_{1} \left (t \right )+5 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 x \left (t \right ) y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 1+5 y \left (t \right ), y^{\prime }\left (t \right ) = 1-6 x \left (t \right )^{2}]
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = 2
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = -x^{3}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime \prime } = \sin \left (x \right )
\] |
✓ |
✓ |
|
|
\[
{}x \sqrt {1+y^{2}}+y \sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\] |
✓ |
✓ |
|
|
\[
{}\sqrt {-x^{2}+1}\, y^{\prime }+\sqrt {1-y^{2}} = 0
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {2 x y}{x^{2}+y^{2}}
\] |
✓ |
✓ |
|
|
\[
{}y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\] |
✓ |
✓ |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
✓ |
✓ |
|
|
\[
{}\left (x +y\right ) y^{\prime } = y-x
\] |
✓ |
✓ |
|