| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (x +12\right ) y = x^{2}+x
\]
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| \[
{} x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (x^{2}+3\right ) y^{\prime }+y = -2 x^{2}+x
\]
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| \[
{} 3 x^{2} \left (1+x \right ) y^{\prime \prime }+x \left (5-x \right ) y^{\prime }+\left (2 x^{2}-1\right ) y = -x^{3}+x
\]
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| \[
{} 9 x^{2} y^{\prime \prime }+\left (2+3 x \right ) y = x^{4}+x^{2}
\]
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| \[
{} 9 x^{2} y^{\prime \prime }+10 x y^{\prime }+y = x -1
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+\left (-x^{2}+x \right ) y^{\prime }-y = x^{3}+1
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 6 \left (-x^{2}+1\right )^{2}
\]
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| \[
{} \left (x^{2}+2 x \right ) y^{\prime \prime }-\left (2 x +2\right ) y^{\prime }+2 y = x^{2} \left (x +2\right )^{2}
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (1+x \right ) y = x \left (x^{2}+x +1\right )
\]
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| \[
{} \left (x^{3}+2 x^{2}\right ) y^{\prime \prime }-x y^{\prime }+\left (1-x \right ) y = x^{2} \left (1+x \right )^{2}
\]
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| \[
{} \left (\cos \left (x \right )^{2}+y \sin \left (2 x \right )\right ) y^{\prime }+y^{2} = 0
\]
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| \[
{} y^{\prime } \left (-x^{2}+1\right )+4 x y = \left (-x^{2}+1\right )^{{3}/{2}}
\]
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| \[
{} \left (y^{3}+x \right ) y^{\prime } = y
\]
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| \[
{} y^{\prime }-\frac {y^{2}}{x^{2}} = {\frac {1}{4}}
\]
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| \[
{} y^{\prime } \sin \left (x \right )+2 y \cos \left (x \right ) = 1
\]
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| \[
{} \left (2 \sin \left (y\right )-x \right ) y^{\prime } = \tan \left (y\right )
\]
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| \[
{} \frac {y^{\prime \prime }}{y}-\frac {{y^{\prime }}^{2}}{y^{2}}+\frac {2 a \coth \left (2 a x \right ) y^{\prime }}{y} = 2 a^{2}
\]
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| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+3 y^{\prime } \left (1+x \right )+y = x^{2}
\]
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| \[
{} \left (x -2\right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}} = 0
\]
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| \[
{} 2 y y^{\prime \prime \prime }+2 \left (3 y^{\prime }+y\right ) y^{\prime \prime }+2 {y^{\prime }}^{2} = \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+6\right ) y = {\mathrm e}^{-x^{2}} \sin \left (2 x \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y}{z^{3}} = 0
\]
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| \[
{} y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+32
\]
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| \[
{} x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\]
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| \[
{} y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\]
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| \[
{} y^{\prime } = \frac {\left (1-y \,{\mathrm e}^{x y}\right ) {\mathrm e}^{-x y}}{x}
\]
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| \[
{} y^{\prime } = \frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )}
\]
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| \[
{} y^{\prime } = y^{3} \sin \left (x \right )
\]
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| \[
{} m v^{\prime } = m g -k v^{2}
\]
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| \[
{} y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\]
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| \[
{} y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\]
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| \[
{} y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\]
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| \[
{} y^{\prime } = \frac {-2 x +4 y}{x +y}
\]
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| \[
{} y^{\prime } = \frac {-\sqrt {x^{2}+y^{2}}+y}{x}
\]
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| \[
{} y^{\prime } = \frac {a y+x}{a x -y}
\]
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| \[
{} y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\]
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| \[
{} \frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\]
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| \[
{} y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\]
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| \[
{} 4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\]
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| \[
{} y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\]
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| \[
{} y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\]
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| \[
{} \sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }+6 y^{\prime }+9 y = \frac {2 \,{\mathrm e}^{-3 x}}{x^{2}+1}
\]
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| \[
{} y^{\prime \prime }-10 y^{\prime }+25 y = \frac {2 \,{\mathrm e}^{5 x}}{x^{2}+4}
\]
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| \[
{} y^{\prime \prime }-2 m y^{\prime }+m^{2} y = \frac {{\mathrm e}^{m x}}{x^{2}+1}
\]
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| \[
{} y^{\prime \prime }+2 y^{\prime }+17 y = \frac {64 \,{\mathrm e}^{-x}}{3+\sin \left (4 x \right )^{2}}
\]
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| \[
{} y^{\prime \prime }+4 y^{\prime }+4 y = \frac {4 \,{\mathrm e}^{-2 x}}{x^{2}+1}+2 x^{2}-1
\]
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| \[
{} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = \frac {2 \,{\mathrm e}^{-x}}{x^{2}+1}
\]
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| \[
{} x y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x -1\right ) y = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+2 y = 8 x^{2} {\mathrm e}^{2 x}
\]
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| \[
{} [x_{1}^{\prime }\left (t \right ) = x_{2} \left (t \right )+3 x_{3} \left (t \right ), x_{2}^{\prime }\left (t \right ) = 2 x_{1} \left (t \right )+3 x_{2} \left (t \right )-2 x_{3} \left (t \right ), x_{3}^{\prime }\left (t \right ) = 2 x_{2} \left (t \right )+2 x_{3} \left (t \right )]
\]
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| \[
{} \left [x_{1}^{\prime }\left (t \right ) = t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}, x_{2}^{\prime }\left (t \right ) = \frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right ), x_{3}^{\prime }\left (t \right ) = \csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-\cos \left (t \right ) t\right ]
\]
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| \[
{} 3 y+y^{\prime } = \left \{\begin {array}{cc} 1 & 0\le t <1 \\ 0 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime }-3 y = \left \{\begin {array}{cc} \sin \left (t \right ) & 0\le t <\frac {\pi }{2} \\ 1 & \frac {\pi }{2}\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }-2 y^{\prime }+5 y = 2 \sin \left (t \right )+\operatorname {Heaviside}\left (t -\frac {\pi }{2}\right ) \left (1+\cos \left (t \right )\right )
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\]
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| \[
{} -y+y^{\prime } = \left \{\begin {array}{cc} 2 & 0\le t <1 \\ -1 & 1\le t \end {array}\right .
\]
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| \[
{} y^{\prime \prime }+2 x^{2} y^{\prime }+x y = 2 \cos \left (x \right )
\]
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| \[
{} y^{\prime \prime }+x y^{\prime }-4 y = 6 \,{\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{\left (-x^{2}+1\right )^{2}}+y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-7 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-x \cos \left (x \right ) y^{\prime }+5 y \,{\mathrm e}^{2 x} = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-\left (x +2\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }-\left (x +5\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+\left (1-x \right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (2 \sqrt {5}-1\right ) x y^{\prime }+\left (\frac {19}{4}-3 x^{2}\right ) y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (-2 x^{5}+9 x \right ) y^{\prime }+\left (10 x^{4}+5 x^{2}+25\right ) y = 0
\]
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| \[
{} 5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0
\]
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| \[
{} 2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\]
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| \[
{} y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\]
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| \[
{} \left (y-x y^{\prime }\right )^{2} = 1+{y^{\prime }}^{2}
\]
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| \[
{} y-x = {y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right )
\]
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| \[
{} y^{\prime }-3 y = {\mathrm e}^{3 x}+{\mathrm e}^{-3 x}
\]
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| \[
{} y y^{\prime } x = \left (1+x \right ) \left (1+y\right )
\]
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| \[
{} y^{\prime } = \frac {2 x -y}{y+2 x}
\]
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| \[
{} y^{\prime } = \frac {3 x -y+1}{3 y-x +5}
\]
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| \[
{} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime } = 0
\]
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| \[
{} \left (x +y^{2}\right ) y^{\prime }+y-x^{2} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y}{x^{2}} = 0
\]
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| \[
{} y^{\prime }+\sin \left (x \right ) y = \sin \left (2 x \right )
\]
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| \[
{} y^{\prime } \sin \left (x \right )+y = \sin \left (2 x \right )
\]
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| \[
{} \sqrt {\left (x +a \right ) \left (x +b \right )}\, \left (2 y^{\prime }-3\right )+y = 0
\]
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| \[
{} \sqrt {\left (x +a \right ) \left (x +b \right )}\, y^{\prime }+y = \sqrt {x +a}-\sqrt {x +b}
\]
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| \[
{} y y^{\prime } x = \sqrt {y^{2}-9}
\]
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| \[
{} \sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (y\right )^{2} y^{\prime } = 0
\]
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| \[
{} y-x^{3}+\left (y^{3}+x \right ) y^{\prime } = 0
\]
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| \[
{} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\]
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| \[
{} \left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right )
\]
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| \[
{} 2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0
\]
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| \[
{} \left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0
\]
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| \[
{} x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0
\]
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| \[
{} x y^{\prime } = \sqrt {x^{2}+y^{2}}
\]
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| \[
{} y^{2} = \left (x^{3}-x y\right ) y^{\prime }
\]
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| \[
{} \left ({\mathrm e}^{x}-3 x^{2} y^{2}\right ) y^{\prime }+y \,{\mathrm e}^{x} = 2 x y^{3}
\]
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| \[
{} y^{2} {\mathrm e}^{x y}+\cos \left (x \right )+\left ({\mathrm e}^{x y}+x y \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\]
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| \[
{} {\mathrm e}^{x} \sin \left (y\right )-y \sin \left (x y\right )+\left ({\mathrm e}^{x} \cos \left (y\right )-x \sin \left (x y\right )\right ) y^{\prime } = 0
\]
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