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ODE |
Mathematica |
Maple |
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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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\[
{} y^{\prime } = 2
\]
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\[
{} y^{\prime } = -x^{3}
\]
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\[
{} y^{\prime \prime } = \sin \left (x \right )
\]
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\[
{} y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}} = 0
\]
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\[
{} \sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } \sqrt {-x^{2}+1}+\sqrt {1-y^{2}} = 0
\]
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\[
{} y^{\prime } = \frac {2 x y}{x^{2}+y^{2}}
\]
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\[
{} y^{\prime } = \frac {y \left (1+\ln \left (y\right )-\ln \left (x \right )\right )}{x}
\]
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\[
{} y^{\prime } x^{2}+y^{2} = x y y^{\prime }
\]
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\[
{} \left (x +y\right ) y^{\prime } = y-x
\]
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\[
{} x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime } = 0
\]
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\[
{} 3 y-7 x +7 = \left (3 x -7 y-3\right ) y^{\prime }
\]
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\[
{} \left (x +2 y+1\right ) y^{\prime } = 3+2 x +4 y
\]
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\[
{} y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y-1\right )^{2}}
\]
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\[
{} \left (x +y\right )^{2} y^{\prime } = a^{2}
\]
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\[
{} x y^{\prime }-4 y = x^{2} \sqrt {y}
\]
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\[
{} \cos \left (x \right ) y^{\prime } = y \sin \left (x \right )+\cos \left (x \right )^{2}
\]
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\[
{} y^{\prime } = 2 x y-x^{3}+x
\]
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\[
{} y^{\prime }+\frac {x y}{x^{2}+1} = \frac {1}{x \left (x^{2}+1\right )}
\]
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\[
{} \left (x -2 x y-y^{2}\right ) y^{\prime }+y^{2} = 0
\]
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\[
{} x y^{\prime }+y = x y^{2} \ln \left (x \right )
\]
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\[
{} y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y} = 0
\]
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\[
{} \left (x^{2} y^{3}+x y\right ) y^{\prime } = 1
\]
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\[
{} x -y^{2}+2 x y y^{\prime } = 0
\]
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\[
{} y^{\prime } = \frac {y^{2}}{3}+\frac {2}{3 x^{2}}
\]
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\[
{} y^{\prime }+y^{2}+\frac {y}{x}-\frac {4}{x^{2}} = 0
\]
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\[
{} x y^{\prime }-3 y+y^{2} = 4 x^{2}-4 x
\]
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\[
{} y^{\prime } = y^{2}+\frac {1}{x^{4}}
\]
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\[
{} \left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime } = \left (1+y^{2}\right )^{{3}/{2}}
\]
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\[
{} y^{\prime } \left (x^{2}+y^{2}+3\right ) = 2 x \left (2 y-\frac {x^{2}}{y}\right )
\]
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\[
{} y^{\prime } = \frac {x -y^{2}}{2 y \left (x +y^{2}\right )}
\]
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\[
{} \left (x \left (x +y\right )+a^{2}\right ) y^{\prime } = y \left (x +y\right )+b^{2}
\]
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\[
{} y^{\prime } = k y+f \left (x \right )
\]
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\[
{} y^{\prime } = y^{2}-x^{2}
\]
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\[
{} \frac {y y^{\prime }+x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y-x y^{\prime }}{x^{2}+y^{2}} = 0
\]
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\[
{} \frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}} = 0
\]
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\[
{} \frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime } = 0
\]
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\[
{} \frac {1}{x}-\frac {y^{2}}{\left (x -y\right )^{2}}+\left (\frac {x^{2}}{\left (x -y\right )^{2}}-\frac {1}{y}\right ) y^{\prime } = 0
\]
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\[
{} y^{3}+2 \left (x^{2}-x y^{2}\right ) y^{\prime } = 0
\]
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\[
{} \left (x^{2} y^{2}-1\right ) y^{\prime }+2 x y^{3} = 0
\]
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\[
{} a x y^{\prime }+b y+x^{m} y^{n} \left (\alpha x y^{\prime }+\beta y\right ) = 0
\]
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\[
{} 2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime } = 0
\]
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\[
{} y^{\prime } = 2 x y-x^{3}+x
\]
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\[
{} y-x y^{2} \ln \left (x \right )+x y^{\prime } = 0
\]
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\[
{} \left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0
\]
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\[
{} y {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-x = 0
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2} = x^{2} y^{2}+x^{4}
\]
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\[
{} {y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+\left (x y^{3}+x^{2} y^{2}+x^{3} y\right ) y^{\prime }-y^{3} x^{3} = 0
\]
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\[
{} {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\]
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\[
{} x {y^{\prime }}^{3} = y^{\prime }+1
\]
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\[
{} {y^{\prime }}^{3}-x^{3} \left (1-y^{\prime }\right ) = 0
\]
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\[
{} {y^{\prime }}^{3}+y^{3}-3 y y^{\prime } = 0
\]
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\[
{} y = {y^{\prime }}^{2} {\mathrm e}^{y^{\prime }}
\]
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\[
{} y^{2} \left (y^{\prime }-1\right ) = \left (2-y^{\prime }\right )^{2}
\]
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\[
{} y \left (1+{y^{\prime }}^{2}\right ) = 2 \alpha
\]
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\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
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\[
{} y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\]
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\[
{} y = \frac {k \left (y y^{\prime }+x \right )}{\sqrt {1+{y^{\prime }}^{2}}}
\]
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\[
{} x = y y^{\prime }+a {y^{\prime }}^{2}
\]
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\[
{} y = {y^{\prime }}^{2} x +{y^{\prime }}^{3}
\]
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\[
{} y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{2}
\]
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\[
{} y = 2 x y^{\prime }+y^{2} {y^{\prime }}^{3}
\]
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\[
{} {y^{\prime }}^{2} \left (x^{2}-1\right )-2 x y y^{\prime }+y^{2}-1 = 0
\]
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\[
{} {y^{\prime }}^{2}+2 x y^{\prime }+2 y = 0
\]
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\[
{} y^{\prime } = \sqrt {y-x}
\]
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\[
{} y^{\prime } = \sqrt {y-x}+1
\]
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\[
{} y^{\prime } = \sqrt {y}
\]
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\[
{} y^{\prime } = y \ln \left (y\right )
\]
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\[
{} y^{\prime } = y \ln \left (y\right )^{2}
\]
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\[
{} y^{\prime } = -x +\sqrt {x^{2}+2 y}
\]
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\[
{} y^{\prime } = -x -\sqrt {x^{2}+2 y}
\]
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\[
{} 4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0
\]
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\[
{} {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0
\]
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\[
{} y^{2} \left (y^{\prime }-1\right ) = \left (2-y^{\prime }\right )^{2}
\]
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\[
{} {y^{\prime }}^{4} = 4 y \left (x y^{\prime }-2 y\right )^{2}
\]
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\[
{} x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 x y = 0
\]
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\[
{} y = {y^{\prime }}^{2}-x y^{\prime }+\frac {x^{3}}{2}
\]
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\[
{} y = 2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2}
\]
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\[
{} {y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\]
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\[
{} {y^{\prime \prime \prime }}^{2}+x^{2} = 1
\]
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\[
{} y^{\prime \prime } = \frac {1}{\sqrt {y}}
\]
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