| # | ODE | Mathematica | Maple | Sympy |
| \[
{} 3 y y^{\prime \prime } = \sin \left (x \right )
\]
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| \[
{} 3 y y^{\prime \prime }+y = 5
\]
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| \[
{} a y y^{\prime \prime }+b y = c
\]
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| \[
{} a y^{2} y^{\prime \prime }+b y^{2} = c
\]
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| \[
{} y^{\prime \prime }-y y^{\prime } = 2 x
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = x
\]
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| \[
{} {y^{\prime \prime }}^{2}+y^{\prime } = 1
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} {y^{\prime \prime }}^{2}+y^{\prime } = x
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = x
\]
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| \[
{} y^{\prime \prime }-6 y^{2}-x = 0
\]
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| \[
{} y^{\prime \prime }+a y^{2}+b x +c = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{3}-x y+a = 0
\]
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| \[
{} y^{\prime \prime }-2 y^{3} a^{2}+2 a b x y-b = 0
\]
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| \[
{} y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\]
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| \[
{} y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\]
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| \[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\]
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| \[
{} y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\]
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| \[
{} y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\]
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| \[
{} y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0
\]
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| \[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\]
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| \[
{} x y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b = 0
\]
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| \[
{} x^{2} y^{\prime \prime }+a \left (x y^{\prime }-y\right )^{2}-b \,x^{2} = 0
\]
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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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| \[
{} 24+12 x y+x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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| \[
{} 2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\]
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| \[
{} 2 \left (-x^{k}+4 x^{3}\right ) \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right )-\left (-12 x^{2}+k \,x^{k -1}\right ) \left (y^{2}+3 y^{\prime }\right )+a x y+b = 0
\]
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| \[
{} y y^{\prime \prime }-a = 0
\]
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| \[
{} y y^{\prime \prime }-a x = 0
\]
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| \[
{} y y^{\prime \prime }-x^{2} a = 0
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2}-a = 0
\]
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| \[
{} y y^{\prime \prime }+y^{2}-a x -b = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\]
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| \[
{} 1+{y^{\prime }}^{2}+2 y y^{\prime \prime } = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+a = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+f \left (x \right ) y^{2}+a = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\]
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| \[
{} 2 y y^{\prime \prime }-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\]
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| \[
{} 2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} 3 y y^{\prime \prime }-2 {y^{\prime }}^{2}-x^{2} a -b x -c = 0
\]
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| \[
{} a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\]
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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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| \[
{} y^{2} y^{\prime \prime }-a = 0
\]
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| \[
{} a x +y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = 0
\]
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| \[
{} y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\]
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| \[
{} x y^{2} y^{\prime \prime }-a = 0
\]
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| \[
{} y^{3} y^{\prime \prime }-a = 0
\]
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\]
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| \[
{} 2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-x^{2} a -b x -c = 0
\]
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| \[
{} \sqrt {y}\, y^{\prime \prime }-a = 0
\]
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| \[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime }-b = 0
\]
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| \[
{} \left (a \sqrt {1+{y^{\prime }}^{2}}-x y^{\prime }\right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\]
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| \[
{} {y^{\prime \prime }}^{2}-a y-b = 0
\]
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| \[
{} y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\]
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| \[
{} y^{\prime } = y^{2}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}
\]
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| \[
{} y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} \left (y^{\prime }-x y^{\prime \prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
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| \[
{} y y^{\prime \prime }-{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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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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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} x^{3} x^{\prime \prime }+1 = 0
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y y^{\prime }+y^{\prime \prime } = 1
\]
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| \[
{} y y^{\prime \prime } = 1
\]
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| \[
{} x y^{\prime \prime }+\left (6 x y^{2}+1\right ) y^{\prime }+2 y^{3}+1 = 0
\]
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| \[
{} \frac {x y^{\prime \prime }}{1+y}+\frac {y y^{\prime }-x {y^{\prime }}^{2}+y^{\prime }}{\left (1+y\right )^{2}} = x \sin \left (x \right )
\]
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| \[
{} y y^{\prime \prime } \sin \left (x \right )+\left (y^{\prime } \sin \left (x \right )+y \cos \left (x \right )\right ) y^{\prime } = \cos \left (x \right )
\]
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| \[
{} \left (\cos \left (y\right )-y \sin \left (y\right )\right ) y^{\prime \prime }-{y^{\prime }}^{2} \left (2 \sin \left (y\right )+y \cos \left (y\right )\right ) = \sin \left (x \right )
\]
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| \[
{} {y^{\prime \prime }}^{2}+{y^{\prime }}^{2} = a^{2}
\]
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| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{2} y^{\prime \prime } = 8 x^{2}
\]
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| \[
{} y^{\prime } y^{\prime \prime } = 1
\]
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| \[
{} x y^{\prime \prime }-{y^{\prime }}^{2} = 6 x^{5}
\]
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| \[
{} y^{\prime } y^{\prime \prime } = 1
\]
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| \[
{} 2 x y^{\prime } y^{\prime \prime } = {y^{\prime }}^{2}-1
\]
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| \[
{} x {y^{\prime \prime }}^{2}+2 y = 2 x
\]
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| \[
{} x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right )
\]
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| \[
{} t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y y^{\prime } = 1
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{3} y^{\prime \prime } = -1
\]
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| \[
{} 1+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime }-\frac {t}{y} = \frac {1}{\pi }
\]
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| \[
{} y^{\prime \prime }+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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| \[
{} y^{\prime \prime }+\frac {y^{\prime }}{5}+y+\frac {y^{3}}{5} = \cos \left (w t \right )
\]
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| \[
{} 2 \left (2 a -y\right ) y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{2} \left (x^{2} y^{\prime \prime }-x y^{\prime }+y\right ) = x^{3}
\]
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| \[
{} x^{2} y^{2} y^{\prime \prime }-3 x y^{2} y^{\prime }+4 y^{3}+x^{6} = 0
\]
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| \[
{} x \left (2 x y+x^{2} y^{\prime }\right ) y^{\prime \prime }+4 x {y^{\prime }}^{2}+8 y y^{\prime } x +4 y^{2}-1 = 0
\]
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| \[
{} x \left (x y+1\right ) y^{\prime \prime }+x^{2} {y^{\prime }}^{2}+\left (4 x y+2\right ) y^{\prime }+y^{2}+1 = 0
\]
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| \[
{} y^{\prime \prime } = x +y^{2}
\]
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