| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{3} y^{\prime \prime } = 1
\]
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| \[
{} y y^{\prime \prime } = 6 x^{4}
\]
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| \[
{} u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right )
\]
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| \[
{} z^{\prime \prime }+{\mathrm e}^{z^{2}} = 1
\]
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| \[
{} y^{3} y^{\prime \prime }+4 = 0
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} y y^{\prime \prime }+1 = {y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+2 {y^{\prime }}^{2} = 2
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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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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| \[
{} y^{\prime \prime } = x +6 y^{2}
\]
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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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| \[
{} 24+12 x y+x^{3} \left (-y^{3}+y y^{\prime }+y^{\prime \prime }\right ) = 0
\]
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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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| \[
{} f \left (x \right )^{2} y^{\prime \prime } = -24 f \left (x \right )^{4}+\left (3 f \left (x \right )^{3}-f \left (x \right )^{2} y+3 f \left (x \right ) f^{\prime }\left (x \right )\right ) y^{\prime }
\]
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| \[
{} y y^{\prime \prime } = a
\]
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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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| \[
{} 3 y y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{3}
\]
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| \[
{} \left (x -{y^{\prime }}^{2}\right ) y^{\prime \prime } = x^{2}-y^{\prime }
\]
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| \[
{} \left ({y^{\prime }}^{2}+a \left (x y^{\prime }-y\right )\right ) y^{\prime \prime } = b
\]
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| \[
{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = 3+{y^{\prime }}^{4}
\]
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| \[
{} h \left (x \right )+g \left (y\right ) y^{\prime }+f \left (y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} {y^{\prime \prime }}^{2} = b y+a
\]
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| \[
{} {y^{\prime \prime }}^{2} = a +b {y^{\prime }}^{2}
\]
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| \[
{} a x -2 y^{\prime } y^{\prime \prime }+x {y^{\prime \prime }}^{2} = 0
\]
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| \[
{} \left (x y^{\prime \prime }-y^{\prime }\right )^{2} = 1+{y^{\prime \prime }}^{2}
\]
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| \[
{} y^{3} y^{\prime \prime } = k
\]
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| \[
{} y y^{\prime \prime } = {y^{\prime }}^{2}-1
\]
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| \[
{} \left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2} = 0
\]
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| \[
{} k = \frac {y^{\prime \prime }}{\left (1+y^{\prime }\right )^{{3}/{2}}}
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2}+4 = 0
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} y y^{\prime \prime }+{y^{\prime }}^{2} = 2
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\]
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| \[
{} \left (2 y+x \right ) y^{\prime \prime }+2 {y^{\prime }}^{2}+2 y^{\prime } = 2
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime } y^{\prime \prime } = x \left (1+x \right )
\]
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| \[
{} 2 y y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime }+{y^{\prime }}^{2} = 1
\]
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| \[
{} y^{\prime \prime } = 1+{y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\]
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| \[
{} {y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\]
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| \[
{} 3 y y^{\prime } y^{\prime \prime } = -1+{y^{\prime }}^{3}
\]
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| \[
{} 4 y {y^{\prime }}^{2} y^{\prime \prime } = 3+{y^{\prime }}^{4}
\]
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| \[
{} y y^{\prime \prime } = 1
\]
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| \[
{} y y^{\prime \prime } = x
\]
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| \[
{} y^{2} y^{\prime \prime } = x
\]
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