| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }+6 x y^{\prime }+6 y = 4 \,{\mathrm e}^{2 x}
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \frac {x^{2}}{\ln \left (x \right )}
\]
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| \[
{} x^{2} y^{\prime \prime }-\left (2 m -1\right ) x y^{\prime }+m^{2} y = x^{m} \ln \left (x \right )^{k}
\]
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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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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 8 x^{4}
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+y = \sqrt {x}\, \ln \left (x \right )
\]
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| \[
{} y^{\prime \prime }+x y = \sin \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}+2
\]
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| \[
{} x y^{\prime \prime } = x +y^{\prime }
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}}
\]
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| \[
{} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x
\]
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| \[
{} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x^{2}}
\]
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| \[
{} x y-x^{2} y^{\prime }+y^{\prime \prime } = x
\]
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| \[
{} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \csc \left (x \right )
\]
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| \[
{} \left (\cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 1+a \csc \left (x \right )
\]
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| \[
{} -y \cos \left (x \right )-y^{\prime } \sin \left (x \right )+y^{\prime \prime } = a -x +x \ln \left (x \right )
\]
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| \[
{} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \left (1+x \right ) \sec \left (x \right )
\]
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| \[
{} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \sin \left (x \right )
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = x^{n}
\]
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| \[
{} -x y+2 y^{\prime }+x y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1
\]
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| \[
{} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}}
\]
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| \[
{} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2}
\]
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| \[
{} x^{2} y^{\prime \prime } = b x +a
\]
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| \[
{} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime } = x^{4}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} a
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x^{2} \left (x +3\right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 3 x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+2 y = x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 4 x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{3} \sin \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 2 x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x^{5} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 2-x
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = x
\]
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| \[
{} x^{2} y^{\prime \prime }+3 x y^{\prime }+y = a -x +x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 5 x
\]
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| \[
{} -5 y-3 x y^{\prime }+x^{2} y^{\prime \prime } = x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = {\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+4 x y^{\prime }+2 y = \ln \left (1+x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{2} \left (x^{2}-1\right )
\]
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| \[
{} a \left (a +1\right ) y-2 a x y^{\prime }+x^{2} y^{\prime \prime } = {\mathrm e}^{x} x^{2+a}
\]
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| \[
{} -2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime } = 1+x +2 x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x \left (x +2\right ) y^{\prime }+\left (x +2\right ) y = x^{3}
\]
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| \[
{} a -x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime } = x
\]
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| \[
{} -y+x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = x \left (-x^{2}+1\right )^{{3}/{2}}
\]
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| \[
{} a -2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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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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| \[
{} n \left (n +1\right ) y-2 x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime } = \frac {2 \left (-n -1\right ) x \operatorname {LegendreP}\left (n , x\right )+2 \left (n +1\right ) \operatorname {LegendreP}\left (n +1, x\right )}{x^{2}-1}
\]
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| \[
{} 2 y+4 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = -2 x +2 \cos \left (x \right )
\]
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| \[
{} 2 y-3 y^{\prime }+\left (1-x \right ) x y^{\prime \prime } = x \left (3 x^{3}+1\right )
\]
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| \[
{} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime } = \cos \left (x \right )
\]
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| \[
{} 6 y-4 y^{\prime } \left (1+x \right )+\left (1+x \right )^{2} y^{\prime \prime } = x
\]
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| \[
{} \left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime } = {\mathrm e}^{x}
\]
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| \[
{} 2 x^{2} y^{\prime \prime }-x y^{\prime }+y = x^{2}
\]
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| \[
{} -2 \left (1-3 x \right ) y-\left (1-4 x \right ) x y^{\prime }+2 x^{2} y^{\prime \prime } = x^{3} \left (1+x \right )
\]
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| \[
{} y-y^{\prime } \left (1+x \right )+2 \left (1+x \right )^{2} y^{\prime \prime } = x
\]
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| \[
{} 4 x^{2} y^{\prime \prime }+y = \sqrt {x}
\]
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| \[
{} -\left (4 x^{2}+1\right ) y+4 x y^{\prime }+4 x^{2} y^{\prime \prime } = 4 x^{{3}/{2}} {\mathrm e}^{x}
\]
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| \[
{} 4 \left (x^{2}+1\right ) y^{\prime \prime } = x^{2}+4 x y^{\prime }
\]
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| \[
{} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 3 x +1
\]
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| \[
{} x^{3} y^{\prime \prime } = b x +a
\]
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| \[
{} x y+3 x^{2} y^{\prime }+x^{3} y^{\prime \prime } = 1
\]
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| \[
{} x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime } = 0
\]
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| \[
{} -x^{2} y^{\prime }+x^{3} y^{\prime \prime } = -x^{2}+3
\]
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| \[
{} \left (c \,x^{2}+2 b x +a \right )^{{3}/{2}} y^{\prime \prime } = f \left (\frac {x}{\sqrt {c \,x^{2}+2 b x +a}}\right )
\]
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| \[
{} f \left (x \right )^{2} y^{\prime \prime } = 3 f \left (x \right )^{3}-a f \left (x \right )^{5}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\]
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| \[
{} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}} = x \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-4 y = x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} {\mathrm e}^{-x}
\]
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| \[
{} 2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = \frac {1}{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } = x^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime } = 1
\]
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| \[
{} x y^{\prime \prime }-y^{\prime } = x^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 8 x^{4}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }-y = x -\frac {1}{x}
\]
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| \[
{} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 2 x^{3}
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 6 x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }+y = 3 x^{2}
\]
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| \[
{} x^{2} y^{\prime \prime }+x y^{\prime }+y = 2 x
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = x
\]
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| \[
{} x y^{\prime \prime }+y^{\prime } = 4 x
\]
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| \[
{} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N = t \ln \left (t \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-x y^{\prime } = x^{3} {\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x +x^{2} \ln \left (x \right )
\]
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| \[
{} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = \ln \left (x \right )^{2}-\ln \left (x^{2}\right )
\]
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| \[
{} \left (1+x \right )^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )-y = \ln \left (1+x \right )^{2}+x -1
\]
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✓ |
✓ |
✗ |
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| \[
{} -12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime } = 6 x
\]
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✓ |
✓ |
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| \[
{} 2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime } = 2
\]
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| \[
{} \left (x^{2}+4\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 8
\]
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| \[
{} \left (1+x \right ) y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+\left (x +2\right ) y = \left (x^{2}+2 x +1\right ) {\mathrm e}^{2 x}
\]
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✓ |
✓ |
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| \[
{} x^{2} y^{\prime \prime }-x \left (2 x +3\right ) y^{\prime }+\left (x^{2}+3 x +3\right ) y = \left (-x^{2}+6\right ) {\mathrm e}^{x}
\]
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| \[
{} x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y = \left (x^{2}-x +1\right ) {\mathrm e}^{x}
\]
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| \[
{} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y = \frac {1}{x^{3}}
\]
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