| # | ODE | Mathematica | Maple | Sympy |
| \[
{} x^{2} y^{\prime \prime }-x y^{\prime }+y = 3 x^{3}
\]
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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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| \[
{} y^{\prime \prime } = x +6 y^{2}
\]
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| \[
{} y^{\prime \prime } = a +b x +c y^{2}
\]
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| \[
{} y^{\prime \prime } = a +b y+2 y^{3}
\]
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| \[
{} y^{\prime \prime } = a +x y+2 y^{3}
\]
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| \[
{} y^{\prime \prime } = f \left (x \right )+g \left (x \right ) y+2 y^{3}
\]
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| \[
{} y^{\prime \prime } = a -2 a b x y+2 y^{3} b^{2}
\]
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| \[
{} y^{\prime \prime } = \operatorname {a0} +\operatorname {a2} y+\operatorname {a1} x y+\operatorname {a3} y^{3}
\]
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| \[
{} y^{\prime \prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}
\]
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| \[
{} y y^{\prime }+y^{\prime \prime } = -12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right )
\]
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| \[
{} y^{\prime \prime } = \operatorname {f2} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f1} \left (x \right ) y^{2}+y^{3}+\left (3 \operatorname {f1} \left (x \right )-y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {g3} \left (x \right )+\operatorname {g2} \left (x \right ) y+\operatorname {g1} \left (x \right ) y^{2}+\operatorname {g0} \left (x \right ) y^{3}+\left (\operatorname {f1} \left (x \right )+\operatorname {f0} \left (x \right ) y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = g \left (x \right )+f \left (x \right ) y^{2}+\left (f \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {f3} \left (x \right )+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = \operatorname {f4} \left (x \right )+\operatorname {f3} \left (x \right ) y+\operatorname {f2} \left (x \right ) y^{2}+\left (\operatorname {f1} \left (x \right )-2 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = a +4 y b^{2}+3 b y^{2}+3 y y^{\prime }
\]
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| \[
{} 3 y y^{\prime }+y^{\prime \prime } = f \left (x \right )+g \left (x \right ) y-y^{3}
\]
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| \[
{} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\]
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| \[
{} y^{\prime \prime } = a^{2}+b^{2} {y^{\prime }}^{2}
\]
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| \[
{} 2 y^{\prime \prime } = 1+12 y^{2}
\]
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| \[
{} 2 y^{\prime }+a \,x^{2} {y^{\prime }}^{2}+x y^{\prime \prime } = b
\]
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| \[
{} \left (-y+a x y^{\prime }\right )^{2}+x y^{\prime \prime } = b
\]
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| \[
{} 2+4 x y^{\prime }+x^{2} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \left (x y^{\prime }-y\right )^{2}+x^{2} y^{\prime \prime } = b \,x^{2}
\]
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| \[
{} 2 x y+a \,x^{4} {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = b
\]
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| \[
{} b x +a y {y^{\prime }}^{2}+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} -x^{2} y^{\prime }+x^{3} y^{\prime \prime } = -x^{2}+3
\]
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| \[
{} 24+12 x y+x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} -6+x y \left (12+3 x y-2 x^{2} y^{2}\right )+x^{2} \left (9+2 x y\right ) y^{\prime }+2 x^{3} y^{\prime \prime } = 0
\]
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| \[
{} 24-48 x y+\left (-12 x^{2}+1\right ) \left (y^{2}+3 y^{\prime }\right )+2 x \left (-4 x^{2}+1\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} b +a x y-\left (-12 x^{2}+k \,x^{k -1}\right ) \left (y^{2}+3 y^{\prime }\right )+2 \left (-4 x^{3}+x^{k}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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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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| \[
{} f \left (x \right )^{2} y^{\prime \prime } = -24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime }
\]
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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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| \[
{} y y^{\prime \prime } = a
\]
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| \[
{} y y^{\prime \prime } = -a^{2}+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = a^{2}
\]
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| \[
{} y y^{\prime \prime } = \operatorname {a0} +\operatorname {a1} y+y^{3} \left (\operatorname {a2} +\operatorname {a3} y\right )+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = b +a {y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2}+\operatorname {a3} y^{2}+\operatorname {a3} y^{3}+\operatorname {a4} y^{4}+a {y^{\prime }}^{2}
\]
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| \[
{} {y^{\prime }}^{2}+\left (a +y\right ) y^{\prime \prime } = b
\]
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| \[
{} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime } = 0
\]
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| \[
{} 2 y y^{\prime \prime } = a +{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -a^{2}-4 \left (-x^{2}+b \right ) y^{2}+8 x y^{3}+3 y^{4}+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -1+2 x f \left (x \right ) y^{2}-y^{4}-4 y^{2} y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} f \left (x \right )+a y y^{\prime }+x {y^{\prime }}^{2}+x y y^{\prime \prime } = 0
\]
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| \[
{} x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 x {y^{\prime }}^{2}+x \left (2 y+x \right ) y^{\prime \prime } = 0
\]
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| \[
{} 3 x y^{2}+6 x^{2} y y^{\prime }+x^{3} {y^{\prime }}^{2}+x^{3} y y^{\prime \prime } = a
\]
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| \[
{} y^{2} y^{\prime \prime } = a
\]
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| \[
{} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = 0
\]
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| \[
{} y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = b x +a
\]
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| \[
{} 2 y^{\prime }+2 y {y^{\prime }}^{2}+\left (x +y^{2}\right ) y^{\prime \prime } = a
\]
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| \[
{} x y^{2} y^{\prime \prime } = a
\]
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| \[
{} y^{3} y^{\prime \prime } = a^{2}
\]
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| \[
{} y^{2} {y^{\prime }}^{2}+2 y^{3} y^{\prime \prime } = 2
\]
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| \[
{} \sqrt {y}\, y^{\prime \prime } = a
\]
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| \[
{} \sqrt {y}\, y^{\prime \prime } = 2 b x +2 a
\]
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| \[
{} X \left (x , y\right )^{3} y^{\prime \prime } = 1
\]
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| \[
{} y^{\prime } y^{\prime \prime } = a^{2} x
\]
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