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# |
ODE |
Mathematica |
Maple |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -6 y \left (t \right ), y^{\prime }\left (t \right ) = 6 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-14]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )-1]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 9 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+2]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 2 x \left (t \right )-10 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+\cos \left (w t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+3, y^{\prime }\left (t \right ) = 7 x \left (t \right )+5 y \left (t \right )+2 t]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+7 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-2 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = {\mathrm e}^{4 t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right ) = {\mathrm e}^{3 t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-2 y \left (t \right ) = 2 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = {\mathrm e}^{-t}, x^{\prime }\left (t \right )+2 x \left (t \right )+y^{\prime }\left (t \right )+y \left (t \right ) = {\mathrm e}^{t}]
\] |
✓ |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-3 x \left (t \right )-y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-4 x \left (t \right )-y \left (t \right ) = {\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-6 y \left (t \right ) = {\mathrm e}^{3 t}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-6 y \left (t \right ) = t]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = 3 t, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )-3 y \left (t \right ) = 1]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 y \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+5 y \left (t \right ) = 4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )+5 y \left (t \right ) = t^{2}, x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-2 x \left (t \right )+4 y \left (t \right ) = 2 t +1]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}+4 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = 2 t^{2}-2 t]
\] |
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\[
{}[3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = t -1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right ) = 2+t]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+4 y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = 3 \,{\mathrm e}^{t}, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{t}]
\] |
✓ |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = -2 t, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+x \left (t \right )-y \left (t \right ) = t^{2}]
\] |
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\[
{}[2 x^{\prime }\left (t \right )+y^{\prime }\left (t \right )-x \left (t \right )-y \left (t \right ) = 1, x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )-y \left (t \right ) = t]
\] |
✓ |
✓ |
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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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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )+5 t, y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )+17 t]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right )-4 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )-4 z \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )-6 y \left (t \right )+6 z \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+7 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = a x \left (t \right )+b y \left (t \right ), y^{\prime }\left (t \right ) = c x \left (t \right )+d y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-4 y \left (t \right )-x \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+4 y \left (t \right )-y \left (t \right ) \left (x \left (t \right )^{2}+y \left (t \right )^{2}\right )]
\] |
✗ |
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\[
{}\left [x^{\prime }\left (t \right ) = y \left (t \right )+\frac {x \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}, y^{\prime }\left (t \right ) = -x \left (t \right )+\frac {y \left (t \right ) \left (1-x \left (t \right )^{2}-y \left (t \right )^{2}\right )}{\sqrt {x \left (t \right )^{2}+y \left (t \right )^{2}}}\right ]
\] |
✗ |
✗ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{2}, y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )+t^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )+\cos \left (2 t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 6 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right )+{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+5 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+\cos \left (3 t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )+{\mathrm e}^{2 t}]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 8 x \left (t \right )+14 y \left (t \right ), y^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = -5 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+20 y \left (t \right ), y^{\prime }\left (t \right ) = 40 x \left (t \right )-19 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -11 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 13 x \left (t \right )-9 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -6 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 13 x \left (t \right ), y^{\prime }\left (t \right ) = 13 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = {\mathrm e}^{2 t}]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = \frac {y \left (t \right )^{2}}{x \left (t \right )}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = \frac {5 x \left (t \right )}{4}+\frac {3 y \left (t \right )}{4}, y^{\prime }\left (t \right ) = \frac {x \left (t \right )}{2}-\frac {3 y \left (t \right )}{2}\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )-x \left (t \right )+2 y \left (t \right ) = 0, y^{\prime }\left (t \right )+y \left (t \right )-x \left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right )+5 x \left (t \right )-2 y \left (t \right ) = 0, 2 x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 0]
\] |
✓ |
✓ |
|