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# |
ODE |
Mathematica |
Maple |
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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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\[
{}\left [x^{\prime }\left (t \right ) = 3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 \pi y \left (t \right )-\frac {x \left (t \right )}{3}\right ]
\] |
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\[
{}\left [p^{\prime }\left (t \right ) = 3 p \left (t \right )-2 q \left (t \right )-7 r \left (t \right ), q^{\prime }\left (t \right ) = -2 p \left (t \right )+6 r \left (t \right ), r^{\prime }\left (t \right ) = \frac {73 q \left (t \right )}{100}+2 r \left (t \right )\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+2 \pi y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = \beta y \left (t \right ), y^{\prime }\left (t \right ) = \gamma x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-5 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 1, y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {x \left (t \right )}{2}, y^{\prime }\left (t \right ) = x \left (t \right )-\frac {y \left (t \right )}{2}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 5 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 9 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )+6 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-5 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-6 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -\frac {9 x \left (t \right )}{10}-2 y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+\frac {11 y \left (t \right )}{10}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-3 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )+4 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )+6 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 y \left (t \right ), y^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}y^{\prime \prime }-6 y^{\prime }-7 y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \frac {y \left (t \right )}{10}, y^{\prime }\left (t \right ) = \frac {z \left (t \right )}{5}, z^{\prime }\left (t \right ) = \frac {2 x \left (t \right )}{5}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right ), z^{\prime }\left (t \right ) = 2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+3 z \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right ), z^{\prime }\left (t \right ) = -3 x \left (t \right )+z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = -y \left (t \right )+2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = -z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -x \left (t \right )+2 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )-4 y \left (t \right ), z^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = -2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = z \left (t \right ), z^{\prime }\left (t \right ) = 0]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = -x \left (t \right )+3 y \left (t \right )-z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -4 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = 5 x \left (t \right )-5 y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = -10 x \left (t \right )+10 y \left (t \right ), y^{\prime }\left (t \right ) = 28 x \left (t \right )-y \left (t \right ), z^{\prime }\left (t \right ) = -\frac {8 z \left (t \right )}{3}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+z \left (t \right ), z^{\prime }\left (t \right ) = z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right ), y^{\prime }\left (t \right ) = -2 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 0, y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
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\[
{}\left [x^{\prime }\left (t \right ) = \pi ^{2} x \left (t \right )+\frac {187 y \left (t \right )}{5}, y^{\prime }\left (t \right ) = \sqrt {555}\, x \left (t \right )+\frac {400617 y \left (t \right )}{5000}\right ]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right )-x \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 x \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = y \left (t \right ), y^{\prime }\left (t \right ) = -4 x \left (t \right )-4 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -3 x \left (t \right )-3 y \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+y \left (t \right )]
\] |
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\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+5 y = 0
\] |
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\[
{}y^{\prime \prime }+2 y^{\prime }+y = 0
\] |
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\[
{}y^{\prime \prime }+2 y = 0
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t}
\] |
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\[
{}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t}
\] |
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\[
{}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t}
\] |
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\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t}
\] |
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