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ODE |
Mathematica |
Maple |
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\[
{}[x^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = 0, y^{\prime }\left (t \right )-x \left (t \right )+3 y \left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right )+x \left (t \right )-z \left (t \right ) = 0, x \left (t \right )+y^{\prime }\left (t \right )-y \left (t \right ) = 0, z^{\prime }\left (t \right )+x \left (t \right )+2 y \left (t \right )-3 z \left (t \right ) = 0]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}+2 y \left (t \right )-3 z \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-\frac {z \left (t \right )}{2}, z^{\prime }\left (t \right ) = -2 x \left (t \right )+z \left (t \right )\right ]
\] |
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\[
{}[x^{\prime }\left (t \right )+y^{\prime }\left (t \right ) = y \left (t \right ), x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = t, x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-t, 2 x^{\prime }\left (t \right )+3 y^{\prime }\left (t \right ) = 2 x \left (t \right )+6]
\] |
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\[
{}[2 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = t, 3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = y \left (t \right )]
\] |
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\[
{}[5 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), 3 x^{\prime }\left (t \right )-y^{\prime }\left (t \right ) = t]
\] |
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\[
{}[x^{\prime }\left (t \right )-4 y^{\prime }\left (t \right ) = 0, 2 x^{\prime }\left (t \right )-3 y^{\prime }\left (t \right ) = y \left (t \right )+t]
\] |
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\[
{}[3 x^{\prime }\left (t \right )+2 y^{\prime }\left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )-2 y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )+t]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+9 y \left (t \right )+12 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+6 y \left (t \right )+6 \,{\mathrm e}^{-t}, y^{\prime }\left (t \right ) = -12 x \left (t \right )+5 y \left (t \right )+37]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+10 y \left (t \right )+18 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -10 x \left (t \right )+9 y \left (t \right )+37]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -14 x \left (t \right )+39 y \left (t \right )+78 \sinh \left (t \right ), y^{\prime }\left (t \right ) = -6 x \left (t \right )+16 y \left (t \right )+6 \cosh \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right )-2 z \left (t \right )-2 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+10 \cosh \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )-2 z \left (t \right )+50 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 6 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )+21 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -x \left (t \right )+6 y \left (t \right )+z \left (t \right )+9]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right )+6 z \left (t \right )+{\mathrm e}^{2 t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+2 z \left (t \right )+2 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = -2 x \left (t \right )+2 y \left (t \right )-2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )+y \left (t \right )-1-6 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right )+4 \,{\mathrm e}^{t}-3]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )+24 \sin \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )+12 \cos \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 7 x \left (t \right )-4 y \left (t \right )+10 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 3 x \left (t \right )+14 y \left (t \right )+6 \,{\mathrm e}^{2 t}]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+4 y \left (t \right )+6 \,{\mathrm e}^{3 t}, y^{\prime }\left (t \right ) = -5 x \left (t \right )+2 y \left (t \right )+6 \,{\mathrm e}^{2 t}]
\] |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )+2 z \left (t \right )+29 \,{\mathrm e}^{-t}, z^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )+z \left (t \right )+39 \,{\mathrm e}^{t}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )-z \left (t \right )+5 \sin \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )-10 \cos \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+z \left (t \right )+2]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+3 y \left (t \right )+z \left (t \right )+5 \sin \left (2 t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right )-3 z \left (t \right )+5 \cos \left (2 t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+7 y \left (t \right )+3 z \left (t \right )+23 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right )-3 z \left (t \right )+2 \,{\mathrm e}^{t}, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2 z \left (t \right )+4 \,{\mathrm e}^{t}, z^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )+3 z \left (t \right )+4 \,{\mathrm e}^{t}]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+5 y \left (t \right )+10 \sinh \left (t \right ), y^{\prime }\left (t \right ) = 19 x \left (t \right )-13 y \left (t \right )+24 \sinh \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 9 x \left (t \right )-3 y \left (t \right )-6 t, y^{\prime }\left (t \right ) = -x \left (t \right )+11 y \left (t \right )+10 t]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )+1, y^{\prime }\left (t \right ) = x \left (t \right )+1]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[4 x^{\prime }\left (t \right )-y^{\prime }\left (t \right )+3 x \left (t \right ) = \sin \left (t \right ), x^{\prime }\left (t \right )+y \left (t \right ) = \cos \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+6 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-10 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 12 x \left (t \right )+18 y \left (t \right ), y^{\prime }\left (t \right ) = -8 x \left (t \right )-12 y \left (t \right )]
\] |
✓ |
✓ |
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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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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )+x -1, y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right )-5 x -2]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}, y_{2}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+1-6 x\right ]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \sin \left (x \right ) y_{1} \left (x \right )+\sqrt {x}\, y_{2} \left (x \right )+\ln \left (x \right ), y_{2}^{\prime }\left (x \right ) = \tan \left (x \right ) y_{1} \left (x \right )-{\mathrm e}^{x} y_{2} \left (x \right )+1\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\] |
✗ |
✗ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = {\mathrm e}^{-x} y_{1} \left (x \right )-\sqrt {1+x}\, y_{2} \left (x \right )+x^{2}, y_{2}^{\prime }\left (x \right ) = \frac {y_{1} \left (x \right )}{\left (x -2\right )^{2}}\right ]
\] |
✗ |
✗ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x}, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x}]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )-2 y_{1} \left (x \right )+\sin \left (2 x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+y_{2} \left (x \right )-2 \cos \left (3 x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{3} \left (x \right )-y_{1} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x, y_{2}^{\prime }\left (x \right ) = {\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right )]
\] |
✗ |
✗ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+4 x -2, y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}\right ]
\] |
✓ |
✓ |
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\[
{}\left [y_{1}^{\prime }\left (x \right ) = \frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}-2 x, y_{2}^{\prime }\left (x \right ) = -\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x}+5 x\right ]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = 3 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = 4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+2 y_{2} \left (x \right )-3 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right )]
\] |
✓ |
✓ |
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\[
{}[y_{1}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right )]
\] |
✓ |
✓ |
|
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\[
{}[y_{1}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )+y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 3 y_{3} \left (x \right )-4 y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 4 y_{3} \left (x \right )+3 y_{4} \left (x \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -3 y_{1} \left (x \right )+2 y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right )-5 y_{3} \left (x \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+2 y_{2} \left (x \right ), y_{2}^{\prime }\left (x \right ) = -2 y_{1} \left (x \right )+3 y_{2} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{3} \left (x \right ), y_{4}^{\prime }\left (x \right ) = 2 y_{4} \left (x \right )]
\] |
✓ |
✓ |
|
|
\[
{}[y_{1}^{\prime }\left (x \right ) = y_{2} \left (x \right )+y_{4} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{1} \left (x \right )-y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = y_{4} \left (x \right ), y_{4}^{\prime }\left (x \right ) = y_{3} \left (x \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )-y \left (t \right )+2, y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )-3]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )-6, y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )+2]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}\left [x^{\prime }\left (t \right ) = 3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 \pi y \left (t \right )-\frac {x \left (t \right )}{3}\right ]
\] |
✓ |
✓ |
|
|
\[
{}\left [p^{\prime }\left (t \right ) = 3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ), q^{\prime }\left (t \right ) = -2 p \left (t \right )+6 r \left (t \right ), r^{\prime }\left (t \right ) = \frac {73 q \left (t \right )}{100}+2 r \left (t \right )\right ]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 \pi y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = \beta y \left (t \right ), y^{\prime }\left (t \right ) = \gamma x \left (t \right )-y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|
|
\[
{}[x^{\prime }\left (t \right ) = 1, y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
✓ |
✓ |
|