| # | ODE | Mathematica | Maple | Sympy |
| \[
{} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime } = 0
\]
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| \[
{} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime } = 0
\]
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| \[
{} a^{2} x^{a -1} y+\left (-2 a +1\right ) x^{a} y^{\prime }+x^{a +1} y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a2} +\operatorname {b2} \,x^{k}\right ) y+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) y^{\prime }+x^{2} \left (\operatorname {a0} +\operatorname {b0} \,x^{k}\right ) y^{\prime \prime } = 0
\]
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| \[
{} \left (\operatorname {a0} +\operatorname {a1} \cos \left (x \right )^{2}\right ) y+a^{2} \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (1-a^{2} \cos \left (x \right )^{2}\right ) y^{\prime \prime } = 0
\]
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| \[
{} -\left (4 k^{2}-\left (-p^{2}+1\right ) \sinh \left (x \right )^{2}\right ) y+4 \cosh \left (x \right ) \sinh \left (x \right ) y^{\prime }+4 \sinh \left (x \right )^{2} y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = a y
\]
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| \[
{} y^{\prime \prime } = 6 y^{2}
\]
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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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| \[
{} y^{\prime \prime } = 2 y^{3}
\]
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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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| \[
{} a \,x^{r} y^{s}+y^{\prime \prime } = 0
\]
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| \[
{} a \sin \left (y\right )+y^{\prime \prime } = 0
\]
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| \[
{} a \,{\mathrm e}^{y}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = f \left (y\right )
\]
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| \[
{} y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+3 f \left (x \right ) y^{\prime }+y^{\prime \prime } = 2 y^{3}
\]
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| \[
{} y^{\prime \prime }+y y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }+y y^{\prime } = y^{3}
\]
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| \[
{} a y+y y^{\prime }+y^{\prime \prime } = y^{3}
\]
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| \[
{} y^{\prime \prime }+y y^{\prime } = -12 f \left (x \right ) y+y^{3}+12 f^{\prime }\left (x \right )
\]
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| \[
{} 2 a^{2} y+a y^{2}+\left (3 a +y\right ) y^{\prime }+y^{\prime \prime } = y^{3}
\]
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| \[
{} y^{\prime \prime } = f \left (x \right ) y^{2}+y^{3}+y \left (-2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+\left (3 f \left (x \right )-y\right ) y^{\prime }
\]
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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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| \[
{} y^{\prime \prime } = f^{\prime }\left (x \right ) y+\left (f \left (x \right )-2 y\right ) y^{\prime }
\]
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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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| \[
{} y^{\prime \prime } = f \left (x \right ) y^{2}-y^{3}+\left (f \left (x \right )-3 y\right ) y^{\prime }
\]
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| \[
{} y^{\prime \prime } = a \left (1+2 y y^{\prime }\right )
\]
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| \[
{} b y+a \left (y^{2}-1\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} g \left (x , y\right )+f \left (x , y\right ) y^{\prime }+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\]
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| \[
{} 2 \cot \left (x \right ) y^{\prime }+2 \tan \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = a {y^{\prime }}^{2}
\]
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| \[
{} y^{\prime \prime } = a^{2}+b^{2} {y^{\prime }}^{2}
\]
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| \[
{} b y+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\]
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| \[
{} f \left (x \right ) y^{\prime }+g \left (x \right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} b y+a y {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} g \left (y\right )+f \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} f \left (x \right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} h \left (y\right )+f \left (y\right ) y^{\prime }+g \left (y\right ) {y^{\prime }}^{2}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime }+{y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = \left (a -x \right ) {y^{\prime }}^{3}
\]
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| \[
{} \left ({\mathrm e}^{2 y}+x \right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} 2 y^{\prime }+4 {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} a {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = x {y^{\prime }}^{3}
\]
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| \[
{} \left (a x +b y\right ) {y^{\prime }}^{3}+y^{\prime \prime } = 0
\]
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| \[
{} a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = a \left (x y^{\prime }-y\right )^{k}
\]
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| \[
{} g \left (x \right ) y^{\prime }+f \left (x \right ) {y^{\prime }}^{k}+y^{\prime \prime } = 0
\]
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| \[
{} y^{\prime \prime } = A \,x^{a} y^{b} {y^{\prime }}^{c}
\]
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| \[
{} y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\]
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| \[
{} y^{\prime \prime } = a \sqrt {b y^{2}+{y^{\prime }}^{2}}
\]
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| \[
{} y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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| \[
{} y^{\prime \prime } = a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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| \[
{} y^{\prime \prime } = a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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| \[
{} y^{\prime \prime } = a y {\left (1+\left (b -y^{\prime }\right )^{2}\right )}^{{3}/{2}}
\]
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| \[
{} y^{\prime \prime } = a \left (b +c x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\]
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| \[
{} y^{3} y^{\prime }+y^{\prime \prime } = y y^{\prime } \sqrt {y^{4}+4 y^{\prime }}
\]
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| \[
{} y^{\prime \prime } = f \left (y^{\prime }\right )
\]
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| \[
{} y^{\prime \prime } = f \left (a x +b y, y^{\prime }\right )
\]
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| \[
{} y^{\prime \prime } = f \left (x , \frac {y^{\prime }}{y}\right ) y
\]
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| \[
{} y^{\prime \prime } = x^{n -2} f \left (y x^{-n}, x^{-n +1} y^{\prime }\right )
\]
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| \[
{} 2 y^{\prime \prime } = 1+12 y^{2}
\]
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| \[
{} 2 y^{\prime \prime } = y \left (a -y^{2}\right )
\]
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| \[
{} 9 {y^{\prime }}^{4}+8 y^{\prime \prime } = 0
\]
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| \[
{} a \,{\mathrm e}^{y} x +y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{5}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} a \,x^{m} y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} b \,{\mathrm e}^{y} x +a y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} \left (-x^{2} a +2\right ) y^{\prime }+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime } = \left (1-y\right ) y^{\prime }
\]
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| \[
{} x {y^{\prime }}^{2}+x y^{\prime \prime } = y^{\prime }
\]
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| \[
{} x y^{\prime \prime } = x {y^{\prime }}^{2}+y^{\prime }
\]
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| \[
{} -2 y^{\prime }+2 x {y^{\prime }}^{2}+x y^{\prime \prime } = 0
\]
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| \[
{} x y^{\prime \prime } = -y^{2}-2 y^{\prime }+x^{2} {y^{\prime }}^{2}
\]
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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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| \[
{} x y^{\prime \prime } = {y^{\prime }}^{3}+y^{\prime }
\]
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| \[
{} 2 y^{\prime }+x y^{\prime \prime } = a \,x^{2 k} {y^{\prime }}^{k}
\]
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| \[
{} y^{\prime }+{y^{\prime }}^{3}+2 x y^{\prime \prime } = 0
\]
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| \[
{} a y \left (1-y^{n}\right )+x^{2} y^{\prime \prime } = 0
\]
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| \[
{} a \,{\mathrm e}^{y-1}+x^{2} y^{\prime \prime } = 0
\]
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