| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{\prime }-x = \operatorname {Heaviside}\left (t -a \right )
\]
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| \[
{} x^{\prime }+x = \operatorname {Heaviside}\left (t -a \right )
\]
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| \[
{} x^{\prime }-x = k \delta \left (t \right )
\]
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| \[
{} x^{\prime \prime }+x = g \left (t \right )
\]
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| \[
{} x^{\prime \prime } = \delta \left (-t +a \right )
\]
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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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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = x \left (t \right )+y \left (t \right ), y^{\prime }\left (t \right ) = -y \left (t \right )+\delta \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 ) = 7 x \left (t \right )-4 y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 4 x \left (t \right )-y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = 3 x \left (t \right )-y \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -2 a x \left (t \right )-y \left (t \right ), y^{\prime }\left (t \right ) = \left (a^{2}+9\right ) x \left (t \right )]
\]
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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 )-5 y \left (t \right )]
\]
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| \[
{} x^{\prime \prime }+2 x^{\prime }-x = 0
\]
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| \[
{} x^{\prime \prime }+2 x^{\prime }+x = 0
\]
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| \[
{} x^{\prime \prime }+2 h x^{\prime }+k^{2} x = 0
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -2 x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-2 x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = a x_{1} \left (t \right )+5 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -3 x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{1} \left (t \right )+x_{2} \left (t \right )+x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{1} \left (t \right )-2 x_{2} \left (t \right )-x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )-x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = a x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = a x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+a x_{3} \left (t \right )]
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{4} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -x_{2} \left (t \right )+x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{2} \left (t \right )+x_{3} \left (t \right ), x_{4}^{\prime }\left (t \right ) = x_{1} \left (t \right )-x_{4} \left (t \right )]
\]
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| \[
{} x^{\prime \prime \prime }+a x^{\prime \prime }+b x^{\prime }+c x = 0
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right ), x_{2}^{\prime }\left (t \right ) = x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = -a x_{3} \left (t \right )-b x_{2} \left (t \right )-c x_{1} \left (t \right )]
\]
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| \[
{} x^{\prime \prime \prime }+x = 0
\]
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| \[
{} x^{\prime \prime \prime }-x = 0
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| \[
{} x^{\prime \prime \prime }+5 x^{\prime \prime }+9 x^{\prime }+5 x = 0
\]
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| \[
{} x^{\prime \prime \prime \prime }+x^{\prime \prime \prime }-x^{\prime }-x = 0
\]
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| \[
{} x^{\prime \prime \prime \prime }+8 x^{\prime \prime \prime }+23 x^{\prime \prime }+2 x^{\prime }+12 x = 0
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| \[
{} x^{\prime } = \lambda x-x^{5}
\]
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| \[
{} x^{\prime } = \lambda x-x^{3}-x^{5}
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = -x_{1} \left (t \right ), x_{2}^{\prime }\left (t \right ) = -2 x_{2} \left (t \right ), x_{3}^{\prime }\left (t \right ) = x_{3} \left (t \right )]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )+y \left (t \right )^{2}, y^{\prime }\left (t \right ) = -2 y \left (t \right )-x \left (t \right )^{2}]
\]
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| \[
{} [x^{\prime }\left (t \right ) = -x \left (t \right )^{3}, y^{\prime }\left (t \right ) = -y \left (t \right )^{3}]
\]
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| \[
{} x^{\prime \prime }-x^{3} = 0
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
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| \[
{} x^{\prime \prime }+6 x^{5} = 0
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| \[
{} x^{\prime \prime }+\lambda x-x^{3} = 0
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
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| \[
{} x^{\prime \prime }+4 x^{3} = 0
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| \[
{} -x^{\prime \prime } = 1-x-x^{2}
\]
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| \[
{} -x^{\prime \prime }+x = {\mathrm e}^{-x}
\]
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| \[
{} -x^{\prime \prime }+x = {\mathrm e}^{-x^{2}}
\]
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| \[
{} -x^{\prime \prime } = \frac {1}{\sqrt {1+x^{2}}}-x
\]
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| \[
{} -x^{\prime \prime } = 2 x-x^{2}
\]
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| \[
{} -x^{\prime \prime } = \arctan \left (x\right )
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| \[
{} y^{\prime } = y
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| \[
{} y^{\prime } = 6 y
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| \[
{} y^{\prime } = -5 y
\]
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| \[
{} y^{\prime } = f \left (x \right ) g \left (y\right )
\]
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| \[
{} x y^{\prime }-y = 0
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| \[
{} y^{\prime }-k y = 0
\]
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| \[
{} y y^{\prime }+x = 0
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| \[
{} x y^{\prime }+y = 0
\]
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| \[
{} -2 y+x y^{\prime } = 0
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| \[
{} \sqrt {x}\, y^{\prime }+1 = 0
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| \[
{} 2 x \left (1+y\right )-y y^{\prime } = 0
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| \[
{} y^{\prime } = -\frac {x}{y}
\]
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| \[
{} y^{\prime } = \frac {2 y}{x}
\]
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| \[
{} -2+2 y+x^{2} \sin \left (y\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {1+x}{1+y^{2}}
\]
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| \[
{} y^{\prime } = \frac {a x +b}{y^{n}+d}
\]
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| \[
{} y^{\prime } = -\frac {x}{y}
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| \[
{} y^{\prime } = x^{2} y
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| \[
{} y^{\prime } = \frac {1+y^{2}}{x^{2}+1}
\]
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| \[
{} x \cos \left (x \right )+\left (1-6 y^{5}\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {x}{y^{3}}
\]
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| \[
{} y^{\prime } = \frac {x}{y^{2} \sqrt {x^{2}+1}}
\]
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| \[
{} y^{\prime } = 2 x y
\]
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| \[
{} x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime } = 0
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| \[
{} y^{\prime } = x^{2} y^{3}
\]
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| \[
{} y^{\prime } = \frac {y \ln \left (x \right )}{x}
\]
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| \[
{} y^{\prime } = x^{2} y
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| \[
{} {\mathrm e}^{x}-y y^{\prime } = 0
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| \[
{} 2 x -6 y+3-\left (1+x -3 y\right ) y^{\prime } = 0
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| \[
{} 2 x +y+1+\left (4 x +2 y+3\right ) y^{\prime } = 0
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| \[
{} 2 x +3 y-1+\left (2 x -3 y+2\right ) y^{\prime } = 0
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| \[
{} x +2 y-4-\left (2 x +y-5\right ) y^{\prime } = 0
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| \[
{} x +2 y-1+3 \left (2 y+x \right ) y^{\prime } = 0
\]
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| \[
{} {\mathrm e}^{-y} \left (1+y^{\prime }\right ) = x \,{\mathrm e}^{x}
\]
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| \[
{} y^{\prime } = \frac {x +y}{x}
\]
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| \[
{} x -y+\left (x -4 y\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}-x y+y^{2}-y y^{\prime } x = 0
\]
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| \[
{} y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\]
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| \[
{} x^{2}-2 y^{2}+y y^{\prime } x = 0
\]
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| \[
{} x y+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y+x y^{\prime }+\frac {y^{3} \left (y-x y^{\prime }\right )}{x} = 0
\]
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| \[
{} \left (x -4\right ) y^{4}-x^{3} \left (y^{2}-3\right ) y^{\prime } = 0
\]
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| \[
{} 1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\]
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| \[
{} x \sin \left (y\right )+\left (x^{2}+1\right ) \cos \left (y\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime }-x y = x^{2}
\]
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| \[
{} y^{\prime } = -\frac {{\mathrm e}^{y}}{x \,{\mathrm e}^{y}+2 y}
\]
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| \[
{} \left (x +y^{2}\right ) y^{\prime }+y = 0
\]
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| \[
{} y^{\prime }+\frac {2 x \sin \left (y\right )+y^{3} {\mathrm e}^{x}}{x^{2} \cos \left (y\right )+3 y^{2} {\mathrm e}^{x}} = 0
\]
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| \[
{} \left (x +y\right ) y^{\prime }+3 x +y = 0
\]
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| \[
{} 3 x \left (x y-2\right )+\left (x^{3}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} 3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = 2 x
\]
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| \[
{} \left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0
\]
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| \[
{} 3 x^{2}+4 x y+\left (2 x^{2}+2 y\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {2 x y \,{\mathrm e}^{\frac {2 x}{y}}}{y^{2}+y^{2} {\mathrm e}^{\frac {2 x}{y}}+2 x^{2} {\mathrm e}^{\frac {2 x}{y}}}
\]
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