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ODE |
Mathematica |
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\[
{}[x^{\prime }\left (t \right ) = -5 x \left (t \right )+3 y \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-4 y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-7 y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -7 x \left (t \right )+y \left (t \right )-6 z \left (t \right ), y^{\prime }\left (t \right ) = 10 x \left (t \right )-4 y \left (t \right )+12 z \left (t \right ), z^{\prime }\left (t \right ) = 2 x \left (t \right )-y \left (t \right )+z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 3 x \left (t \right )+2 y \left (t \right )+4 z \left (t \right ), y^{\prime }\left (t \right ) = 2 x \left (t \right )+2 z \left (t \right ), z^{\prime }\left (t \right ) = 4 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -x \left (t \right )-3 y \left (t \right )-z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )-z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = -2 x \left (t \right )+y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -3 x \left (t \right )+2 y \left (t \right )+3 z \left (t \right ), z^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right )-2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right ), z^{\prime }\left (t \right ) = 2 h \left (t \right ), h^{\prime }\left (t \right ) = -2 z \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 2 y \left (t \right )+z \left (t \right ), y^{\prime }\left (t \right ) = -2 x \left (t \right )+h \left (t \right ), z^{\prime }\left (t \right ) = 2 h \left (t \right ), h^{\prime }\left (t \right ) = -2 z \left (t \right )]
\] |
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\[
{}x^{\prime } = x \left (1-x\right )
\] |
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\[
{}x^{\prime } = -x \left (1-x\right )
\] |
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\[
{}x^{\prime } = x^{2}
\] |
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\[
{}\left [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -\frac {\left (x_{1} \left (t \right )^{2}+\sqrt {x_{1} \left (t \right )^{2}+4 x_{2} \left (t \right )^{2}}\right ) x_{1} \left (t \right )}{2}\right ]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right )-x_{2} \left (t \right )+1, x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )-x_{2} \left (t \right )+5]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )-x \left (t \right )^{3}-x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 2 y \left (t \right )-y \left (t \right )^{5}-y \left (t \right ) x \left (t \right )^{4}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}+1, y^{\prime }\left (t \right ) = x \left (t \right )^{2}-y \left (t \right )^{2}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = x \left (t \right )^{2}+y \left (t \right )^{2}-1, y^{\prime }\left (t \right ) = 2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = 6 x \left (t \right )-6 x \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right ), y^{\prime }\left (t \right ) = 4 y \left (t \right )-4 y \left (t \right )^{2}-2 x \left (t \right ) y \left (t \right )]
\] |
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\[
{}[x^{\prime }\left (t \right ) = \tan \left (x \left (t \right )+y \left (t \right )\right ), y^{\prime }\left (t \right ) = x \left (t \right )+x \left (t \right )^{3}]
\] |
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\[
{}[x^{\prime }\left (t \right ) = {\mathrm e}^{y \left (t \right )}-x \left (t \right ), y^{\prime }\left (t \right ) = {\mathrm e}^{x \left (t \right )}+y \left (t \right )]
\] |
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\[
{}z^{\prime \prime }+z^{3} = 0
\] |
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\[
{}z^{\prime \prime }+z+z^{5} = 0
\] |
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\[
{}z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\] |
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\[
{}z^{\prime \prime }+\frac {z}{1+z^{2}} = 0
\] |
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\[
{}z^{\prime \prime }+z-2 z^{3} = 0
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-5 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 8 x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+5 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = -4 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-6 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )-4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -8 x_{1} \left (t \right )+4 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 3 x_{1} \left (t \right )-x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 5 x_{1} \left (t \right )-3 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )-x_{2} \left (t \right )]
\] |
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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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\[
{}[x_{1}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -5 x_{1} \left (t \right )-2 x_{2} \left (t \right )]
\] |
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\[
{}[x_{1}^{\prime }\left (t \right ) = 4 x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -9 x_{1} \left (t \right )]
\] |
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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}y^{\prime \prime }-\lambda y = 0
\] |
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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}y^{\prime \prime }-2 y^{\prime }+\left (\lambda +1\right ) y = 0
\] |
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\[
{}y^{\prime \prime }+\lambda y = 0
\] |
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\[
{}x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0
\] |
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\[
{}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
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\[
{}y+x y^{\prime } = 0
\] |
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\[
{}y^{\prime } = 2 x y
\] |
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\[
{}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0
\] |
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\[
{}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0
\] |
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\[
{}\left (1+x \right ) y^{\prime }-1+y = 0
\] |
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\[
{}\tan \left (x \right ) y^{\prime }-y = 1
\] |
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\[
{}y+3+\cot \left (x \right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {x}{y}
\] |
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\[
{}x^{\prime } = 1-\sin \left (2 t \right )
\] |
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\[
{}y+x y^{\prime } = y^{2}
\] |
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\[
{}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0
\] |
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\[
{}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime }
\] |
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\[
{}y+x y^{\prime } = x y \left (y^{\prime }-1\right )
\] |
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\[
{}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0
\] |
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\[
{}y = x y+x^{2} y^{\prime }
\] |
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\[
{}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0
\] |
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\[
{}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0
\] |
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\[
{}y^{\prime } = \frac {y}{x}
\] |
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\[
{}x y^{\prime }+2 y = 0
\] |
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\[
{}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0
\] |
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\[
{}x^{2} y^{\prime }+y^{2} = 0
\] |
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\[
{}y^{\prime } = {\mathrm e}^{y}
\] |
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\[
{}{\mathrm e}^{y} \left (1+y^{\prime }\right ) = 1
\] |
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\[
{}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (x -1\right )}
\] |
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\[
{}x^{2}+3 x y^{\prime } = y^{3}+2 y
\] |
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\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
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\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
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\[
{}x +y = x y^{\prime }
\] |
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\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
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\[
{}x y^{\prime }-y = \sqrt {x y}
\] |
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\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
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\[
{}x y^{\prime }-y = \sqrt {x^{2}-y^{2}}
\] |
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\[
{}x +y y^{\prime } = 2 y
\] |
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\[
{}x y^{\prime }-y+\sqrt {y^{2}-x^{2}} = 0
\] |
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\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
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\[
{}\left (x y-x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
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\[
{}y+x y^{\prime } = 2 \sqrt {x y}
\] |
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\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
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\[
{}y \left (x^{2}-x y+y^{2}\right )+x y^{\prime } \left (y^{2}+x y+x^{2}\right ) = 0
\] |
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\[
{}x y^{\prime }-y-\sin \left (\frac {y}{x}\right ) x = 0
\] |
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\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
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\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
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\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
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\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y = x y^{\prime }
\] |
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\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
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\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
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\[
{}\left (3 x y-2 x^{2}\right ) y^{\prime } = 2 y^{2}-x y
\] |
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\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
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\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
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\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
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\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
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\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
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\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
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\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
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\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
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\[
{}y^{\prime } = \frac {x +y-1}{-y+x -1}
\] |
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\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
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