| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime }-f \left (x \right ) y^{\prime }+\left (f \left (x \right )-1\right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }+x^{3} y = 0
\]
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| \[
{} y^{\prime \prime }+3 x y^{\prime }+x^{2} y = 0
\]
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| \[
{} y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}}
\]
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2}
\]
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| \[
{} \left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (x +2\right ) y = x \left (1+x \right )^{2}
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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| \[
{} y-y^{\prime } \left (1+x \right )+x y^{\prime \prime } = x^{2} {\mathrm e}^{2 x}
\]
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| \[
{} x y^{\prime } = y
\]
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| \[
{} x^{2} y^{\prime } = y
\]
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| \[
{} y+x y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} x^{3} \left (x -1\right ) y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+3 x y = 0
\]
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| \[
{} x^{2} \left (x^{2}-1\right )^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0
\]
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| \[
{} x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0
\]
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| \[
{} x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0
\]
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| \[
{} y^{\prime \prime }+\frac {n y^{\prime }}{x^{2}}+\frac {q y}{x^{3}} = 0
\]
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| \[
{} x y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-\left (9+4 x \right ) y = 0
\]
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| \[
{} x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+\left (x +3\right ) y = 3 \,{\mathrm e}^{-x}
\]
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| \[
{} y^{\prime \prime }+x^{2} y = 0
\]
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| \[
{} x^{\prime \prime }+\left (5 x^{4}-9 x^{2}\right ) x^{\prime }+x^{5} = 0
\]
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| \[
{} x^{\prime } = x^{2}-3 x+2
\]
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| \[
{} x^{\prime } = \left (x-1\right )^{2}
\]
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| \[
{} x^{\prime } = 2 \sqrt {x}
\]
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| \[
{} 2 t +3 x+\left (3 t -x\right ) x^{\prime } = t^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }-\frac {x^{2} {y^{\prime }}^{2}}{2 y}+4 x y^{\prime }+4 y = 0
\]
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| \[
{} \sin \left (x \right ) y^{\prime \prime }+\cos \left (x \right ) y^{\prime }+n y \sin \left (x \right ) = 0
\]
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| \[
{} v^{\prime \prime } = \left (\frac {1}{v}+{v^{\prime }}^{4}\right )^{{1}/{3}}
\]
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| \[
{} \sqrt {y^{\prime }+y} = \left (y^{\prime \prime }+2 x \right )^{{1}/{4}}
\]
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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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| \[
{} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime } = g
\]
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| \[
{} y y^{\prime }+x = m y
\]
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| \[
{} \frac {2 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime } = 0
\]
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| \[
{} \left (T+\frac {1}{\sqrt {t^{2}-T^{2}}}\right ) T^{\prime } = \frac {T}{t \sqrt {t^{2}-T^{2}}}-t
\]
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| \[
{} x {y^{\prime }}^{2}+2 y^{\prime }-y = 0
\]
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| \[
{} \sqrt {t^{2}+T} = T^{\prime }
\]
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| \[
{} y^{\prime \prime } = \frac {m \sqrt {1+{y^{\prime }}^{2}}}{k}
\]
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| \[
{} \phi ^{\prime \prime } = \frac {4 \pi n c}{\sqrt {v_{0}^{2}+\frac {2 e \left (\phi -V_{0} \right )}{m}}}
\]
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| \[
{} 4 {y^{\prime }}^{3} y-2 x^{2} {y^{\prime }}^{2}+4 y y^{\prime } x +x^{3} = 16 y^{2}
\]
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| \[
{} y^{\prime \prime } = c \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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| \[
{} 1+{y^{\prime }}^{2}+\frac {m y^{\prime \prime }}{\sqrt {1+{y^{\prime }}^{2}}} = 0
\]
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| \[
{} y = x y^{\prime }+y^{\prime }-{y^{\prime }}^{3}
\]
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| \[
{} y^{\prime \prime }-2 y y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }-{y^{\prime }}^{2}-{y^{\prime }}^{3} y = 0
\]
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| \[
{} \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = r y^{\prime \prime }
\]
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| \[
{} y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime \prime }}^{2}+3 y^{\prime \prime } {y^{\prime }}^{2}-2 {y^{\prime }}^{4}-x {y^{\prime }}^{5} = 0
\]
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| \[
{} \left (1+y^{2}\right ) y^{\prime \prime }-2 y {y^{\prime }}^{2}-2 \left (1+y^{2}\right ) y^{\prime } = y^{2} \left (1+y^{2}\right )
\]
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| \[
{} y^{2} y^{\prime \prime \prime }-\left (3 y y^{\prime }+2 x y^{2}\right ) y^{\prime \prime }+\left (2 {y^{\prime }}^{2}+2 y y^{\prime } x +3 x^{2} y^{2}\right ) y^{\prime }+x^{3} y^{3} = 0
\]
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| \[
{} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}} = 0
\]
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| \[
{} \sqrt {2 a y-y^{2}}\, \csc \left (x \right )+y \tan \left (x \right ) y^{\prime } = 0
\]
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| \[
{} x^{3}-3 x^{2} y+5 x y^{2}-7 y^{3}+\left (y^{4}+2 y^{2}-x^{3}+5 x^{2} y-21 x y^{2}\right ) y^{\prime } = 0
\]
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| \[
{} x^{3}+4 x y+y^{2}+\left (2 x^{2}+2 x y+4 y^{3}\right ) y^{\prime } = 0
\]
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| \[
{} x \left (x -2 y\right ) y^{\prime }+x^{2}+2 y^{2} = 0
\]
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| \[
{} \left (x^{2}+2 x y\right ) y^{\prime }-3 x^{2}+2 x y-y^{2} = 0
\]
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| \[
{} \left (6 x -5 y+4\right ) y^{\prime } = 1+2 x -y
\]
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| \[
{} \left (5 x -2 y+7\right ) y^{\prime } = x -3 y+2
\]
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| \[
{} \left (x^{2}-1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 2 x
\]
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| \[
{} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = x
\]
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| \[
{} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\csc \left (x \right )^{2} y = \cos \left (x \right )
\]
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| \[
{} \left (x^{2}-x \right ) y^{\prime \prime }+\left (3 x -2\right ) y^{\prime }+y = 0
\]
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| \[
{} \left (3 x^{2}+x \right ) y^{\prime \prime }+2 \left (1+6 x \right ) y^{\prime }+6 y = \sin \left (x \right )
\]
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| \[
{} \left (x^{3}+x^{2}-3 x +1\right ) y^{\prime \prime \prime }+\left (9 x^{2}+6 x -9\right ) y^{\prime \prime }+\left (18 x +6\right ) y^{\prime }+6 y = x^{3}
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2} = 1
\]
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| \[
{} \left (3 x +4 y\right ) y^{\prime }+y-2 x = 0
\]
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| \[
{} \left (y-3 x +3\right ) y^{\prime } = 2 y-x -4
\]
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| \[
{} x^{2}-4 x y-2 y^{2}+\left (y^{2}-4 x y-2 x^{2}\right ) y^{\prime } = 0
\]
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| \[
{} x +y y^{\prime }+\frac {x y^{\prime }-y}{x^{2}+y^{2}} = 0
\]
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| \[
{} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime } = 0
\]
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| \[
{} \left (2 x^{2} y+4 x^{3}-12 x y^{2}+3 y^{2}-x \,{\mathrm e}^{y}+{\mathrm e}^{2 x}\right ) y^{\prime }+12 x^{2} y+2 x y^{2}+4 x^{3}-4 y^{3}+2 y \,{\mathrm e}^{2 x}-{\mathrm e}^{y} = 0
\]
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| \[
{} 3 x^{2} y^{4}+2 x y+\left (2 x^{3} y^{3}-x^{2}\right ) y^{\prime } = 0
\]
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| \[
{} 2 x^{2} y-3 y^{4}+\left (3 x^{3}+2 x y^{3}\right ) y^{\prime } = 0
\]
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| \[
{} y^{2}+2 x^{2} y+\left (2 x^{3}-x y\right ) y^{\prime } = 0
\]
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| \[
{} x y^{\prime }-y = x \sqrt {x^{2}+y^{2}}
\]
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| \[
{} y^{\prime }+\frac {y}{\sqrt {-x^{2}+1}} = \frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}
\]
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| \[
{} x \left (-a^{2}+x^{2}+y^{2}\right )+y \left (x^{2}-y^{2}-b^{2}\right ) y^{\prime } = 0
\]
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| \[
{} y y^{\prime }+x = m \left (x y^{\prime }-y\right )
\]
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| \[
{} y+\left (a \,x^{2} y^{n}-2 x \right ) y^{\prime } = 0
\]
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| \[
{} \left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime } = 3 x y^{2}-x^{2}
\]
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| \[
{} y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right ) = 0
\]
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| \[
{} y^{\prime }+\frac {n y}{x} = a \,x^{-n}
\]
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| \[
{} x -y y^{\prime } = a {y^{\prime }}^{2}
\]
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| \[
{} y = -a y^{\prime }+\frac {c +a \arcsin \left (y^{\prime }\right )}{\sqrt {1-{y^{\prime }}^{2}}}
\]
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| \[
{} 4 y = {y^{\prime }}^{2}+x^{2}
\]
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| \[
{} x^{2} \left (y-x y^{\prime }\right ) = y {y^{\prime }}^{2}
\]
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| \[
{} y = x y^{\prime }+\arcsin \left (y^{\prime }\right )
\]
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| \[
{} {\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2} = 0
\]
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| \[
{} y = y^{\prime } \left (x -b \right )+\frac {a}{y^{\prime }}
\]
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| \[
{} a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0
\]
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| \[
{} \left (x y^{\prime }-y\right )^{2} = a \left (1+{y^{\prime }}^{2}\right ) \left (x^{2}+y^{2}\right )^{{3}/{2}}
\]
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| \[
{} \left (x y^{\prime }-y\right )^{2} = {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+1
\]
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| \[
{} \left (x^{2}+y^{2}\right ) \left (1+y^{\prime }\right )^{2}-2 \left (x +y\right ) \left (1+y^{\prime }\right ) \left (y y^{\prime }+x \right )+\left (y y^{\prime }+x \right )^{2} = 0
\]
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| \[
{} \left (x y^{\prime }-y\right ) \left (y y^{\prime }+x \right ) = h^{2} y^{\prime }
\]
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| \[
{} {y^{\prime }}^{3}-4 y y^{\prime } x +8 y^{2} = 0
\]
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| \[
{} {y^{\prime }}^{3}+m {y^{\prime }}^{2} = a \left (y+m x \right )
\]
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| \[
{} {\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3} = 0
\]
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| \[
{} \left (1-y^{2}+\frac {y^{4}}{x^{2}}\right ) {y^{\prime }}^{2}-\frac {2 y y^{\prime }}{x}+\frac {y^{2}}{x^{2}} = 0
\]
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| \[
{} y = x y^{\prime }+\frac {m}{y^{\prime }}
\]
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