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# |
ODE |
Mathematica |
Maple |
Sympy |
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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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\[
{} \left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-\frac {x_{2} \left (t \right )}{4}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-\frac {x_{2} \left (t \right )}{2}\right ]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}-x_{2} \left (t \right )\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )+x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+\frac {5 x_{2} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = -\frac {5 x_{1} \left (t \right )}{2}+2 x_{2} \left (t \right )\right ]
\]
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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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\[
{} [x_{1}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-5 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )+3 x_{2} \left (t \right )]
\]
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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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\[
{} [x_{1}^{\prime }\left (t \right ) = -k_{1} x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = k_{1} x_{1} \left (t \right )-k_{2} x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = k_{2} x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-2 x_{2} \left (t \right )+t]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+\sqrt {3}\, x_{2} \left (t \right )+{\mathrm e}^{t}, x_{2}^{\prime }\left (t \right ) = \sqrt {3}\, x_{1} \left (t \right )-x_{2} \left (t \right )+\sqrt {3}\, {\mathrm e}^{-t}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-5 x_{2} \left (t \right )-\cos \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+\sin \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+{\mathrm e}^{-2 t}, x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-2 x_{2} \left (t \right )-2 \,{\mathrm e}^{t}]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 1-x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )+3 x_{3} \left (t \right )+{\mathrm e}^{-t}]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}-\frac {x_{3} \left (t \right )}{2}+1, x_{2}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right )+t, x_{3}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+\frac {x_{2} \left (t \right )}{2}-\frac {3 x_{3} \left (t \right )}{2}+11 \,{\mathrm e}^{-3 t}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right )+3 t, x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right )+3 \cos \left (t \right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = -\frac {x_{1} \left (t \right )}{2}+x_{2} \left (t \right )+\frac {x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )+x_{3} \left (t \right )-\sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \frac {x_{1} \left (t \right )}{2}+x_{2} \left (t \right )-\frac {x_{3} \left (t \right )}{2}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-9 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{1} \left (t \right )+2 x_{2} \left (t \right )+4 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-5 x_{2} \left (t \right )-4 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )+3 x_{2} \left (t \right )+3 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -7 x_{1} \left (t \right )+9 x_{2} \left (t \right )-6 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+11 x_{2} \left (t \right )-7 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )+6 x_{2} \left (t \right )+2 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )-16 x_{2} \left (t \right )-16 x_{3} \left (t \right )-17 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-10 x_{2} \left (t \right )-8 x_{3} \left (t \right )-7 x_{4} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-2 x_{3} \left (t \right )-3 x_{4} \left (t \right ), x_{4}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+14 x_{2} \left (t \right )+14 x_{3} \left (t \right )+14 x_{4} \left (t \right )]
\]
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\[
{} \left [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )-2 x_{3} \left (t \right )+3 x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-\frac {3 x_{2} \left (t \right )}{2}-x_{3} \left (t \right )+\frac {7 x_{4} \left (t \right )}{2}, x_{3}^{\prime }\left (t \right ) = -x_{1} \left (t \right )+\frac {x_{2} \left (t \right )}{2}-\frac {3 x_{4} \left (t \right )}{2}, x_{4}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+\frac {3 x_{2} \left (t \right )}{2}+3 x_{3} \left (t \right )-\frac {7 x_{4} \left (t \right )}{2}\right ]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-7 x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{2} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )+x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 6 x_{1} \left (t \right )+4 x_{2} \left (t \right )+6 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )-4 x_{3} \left (t \right )]
\]
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\[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -14 x_{1} \left (t \right )-5 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 15 x_{1} \left (t \right )+5 x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = -2 y \left (t \right )+x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+4 x \left (t \right ) y \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right ) = 1+5 y \left (t \right ), y^{\prime }\left (t \right ) = 1-6 x \left (t \right )^{2}]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )]
\]
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\[
{} [y^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )+z \left (x \right )+x]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )}{2}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = 1-\frac {1}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {1}{y \left (x \right )-x}\right ]
\]
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\[
{} [y^{\prime }\left (x \right ) = -z \left (x \right ), z^{\prime }\left (x \right ) = y \left (x \right )]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}, z^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}\right ]
\]
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\[
{} \left [y^{\prime }\left (x \right ) = \frac {y \left (x \right )^{2}}{z \left (x \right )}, z^{\prime }\left (x \right ) = \frac {z \left (x \right )^{2}}{y \left (x \right )}\right ]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right )+z \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\]
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\[
{} [x^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = t^{2}, y^{\prime }\left (t \right )+y \left (t \right )+z \left (t \right ) = 2 t, z^{\prime }\left (t \right )+z \left (t \right ) = t]
\]
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\[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = 7 \,{\mathrm e}^{t}-27, y^{\prime }\left (t \right )-2 x \left (t \right )+3 y \left (t \right ) = -3 \,{\mathrm e}^{t}+12]
\]
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\[
{} [y^{\prime \prime }\left (x \right )+z^{\prime }\left (x \right )-2 z \left (x \right ) = {\mathrm e}^{2 x}, z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )-3 y \left (x \right ) = 0]
\]
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\[
{} [x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+{\mathrm e}^{t}+{\mathrm e}^{-t}]
\]
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\[
{} \left [y^{\prime }\left (x \right )+\frac {2 z \left (x \right )}{x^{2}} = 1, z^{\prime }\left (x \right )+y \left (x \right ) = x\right ]
\]
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\[
{} [t x^{\prime }\left (t \right )-x \left (t \right )-3 y \left (t \right ) = t, t y^{\prime }\left (t \right )-x \left (t \right )+y \left (t \right ) = 0]
\]
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\[
{} [t x^{\prime }\left (t \right )+6 x \left (t \right )-y \left (t \right )-3 z \left (t \right ) = 0, t y^{\prime }\left (t \right )+23 x \left (t \right )-6 y \left (t \right )-9 z \left (t \right ) = 0, t z^{\prime }\left (t \right )+x \left (t \right )+y \left (t \right )-2 z \left (t \right ) = 0]
\]
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✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right )+5 x \left (t \right )+y \left (t \right ) = {\mathrm e}^{t}, y^{\prime }\left (t \right )+3 y \left (t \right )-x \left (t \right ) = {\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )+t -1, y^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )-5 t -2]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 7 x \left (t \right )+6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-5 t +2, y^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right )-8 t -8]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = 3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -17 x \left (t \right )-5 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = -4 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 8 x \left (t \right )-6 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = 5 x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+2 y \left (t \right )]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+7 y \left (x \right )-3 z \left (x \right ) = 0, 7 y^{\prime }\left (x \right )+63 y \left (x \right )-36 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+2 y^{\prime }\left (x \right )+3 y \left (x \right ) = 0, y^{\prime }\left (x \right )+3 y \left (x \right )-2 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+3 y \left (x \right )+z \left (x \right ) = 0, z^{\prime }\left (x \right )+3 y \left (x \right )+5 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+3 y \left (x \right )+2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+2 y \left (x \right )-4 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )-3 y \left (x \right )-2 z \left (x \right ) = 0, z^{\prime }\left (x \right )+y \left (x \right )-2 z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )+z^{\prime }\left (x \right )+6 y \left (x \right ) = 0, z^{\prime }\left (x \right )+5 y \left (x \right )+z \left (x \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+y^{\prime }\left (x \right )+5 y \left (x \right )-3 z \left (x \right ) = x +{\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+y \left (x \right )+3 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+3 y \left (x \right )+4 z \left (x \right ) = {\mathrm e}^{2 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )-3 y \left (x \right )+2 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )+2 y \left (x \right )-z \left (x \right ) = {\mathrm e}^{3 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = x, y^{\prime }\left (x \right )+4 y \left (x \right )+z \left (x \right ) = x]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [z^{\prime }\left (x \right )+7 y \left (x \right )-9 z \left (x \right ) = {\mathrm e}^{x}, y^{\prime }\left (x \right )-y \left (x \right )-3 z \left (x \right ) = {\mathrm e}^{2 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [y^{\prime }\left (x \right )-2 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{3 x}, z^{\prime }\left (x \right )+5 y \left (x \right )-2 z \left (x \right ) = {\mathrm e}^{4 x}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right )+y^{\prime }\left (t \right )+2 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )+5 x \left (t \right )+3 y \left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right )-7 x \left (t \right )+y \left (t \right ) = 0, y^{\prime }\left (t \right )-2 x \left (t \right )-5 y \left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime }\left (t \right )+2 x \left (t \right )-3 y \left (t \right ) = t, y^{\prime }\left (t \right )-3 x \left (t \right )+2 y \left (t \right ) = {\mathrm e}^{2 t}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [4 x^{\prime }\left (t \right )+9 y^{\prime }\left (t \right )+44 x \left (t \right )+49 y \left (t \right ) = t, 3 x^{\prime }\left (t \right )+7 y^{\prime }\left (t \right )+34 x \left (t \right )+38 y \left (t \right ) = {\mathrm e}^{t}]
\]
|
✓ |
✓ |
✓ |
|
|
\[
{} [x^{\prime \prime }\left (t \right )-3 x \left (t \right )-4 y \left (t \right ) = 0, y^{\prime \prime }\left (t \right )+x \left (t \right )+y \left (t \right ) = 0]
\]
|
✓ |
✓ |
✓ |
|