| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime \prime } = f \left (a x +b y, y^{\prime }\right )
\]
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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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| \[
{} x y^{n}+2 y^{\prime }+x y^{\prime \prime } = 0
\]
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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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| \[
{} \left (-y+a x y^{\prime }\right )^{2}+x y^{\prime \prime } = b
\]
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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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| \[
{} \left (a +1\right ) x y^{\prime }+x^{2} y^{\prime \prime } = x^{k} f \left (x^{k} y, k y+x y^{\prime }\right )
\]
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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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| \[
{} -6+x y \left (12+3 x y-2 x^{2} y^{2}\right )+x^{2} \left (9+2 x y\right ) y^{\prime }+2 x^{3} y^{\prime \prime } = 0
\]
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| \[
{} y^{b}+x^{a} y^{\prime \prime } = 0
\]
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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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| \[
{} \sqrt {x}\, y^{\prime \prime } = y^{{3}/{2}}
\]
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| \[
{} f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right )^{2} y^{\prime \prime } = g \left (y, f \left (x \right ) y^{\prime }\right )
\]
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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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| \[
{} y y^{\prime \prime } = {\mathrm e}^{x} y \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+{\mathrm e}^{2 x} \left (\operatorname {a2} +\operatorname {a3} y^{4}\right )+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = y^{2} \left (f \left (x \right ) y+g^{\prime }\left (x \right )\right )+y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} y-x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} a x y^{\prime }+{y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} y y^{\prime \prime } = b y^{2}+y^{3}+a y y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} y y^{\prime \prime } = -y \left (f^{\prime }\left (x \right )-y^{2} g^{\prime }\left (x \right )\right )+\left (f \left (x \right )+g \left (x \right ) y^{2}\right ) y^{\prime }+{y^{\prime }}^{2}
\]
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| \[
{} g \left (x \right ) y^{2}+f \left (x \right ) y y^{\prime }+a {y^{\prime }}^{2}+y y^{\prime \prime } = 0
\]
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| \[
{} 2 y y^{\prime \prime } = 4 y^{2} \left (2 y+x \right )+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = -1-2 x y^{2}+a y^{3}+{y^{\prime }}^{2}
\]
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| \[
{} 2 y y^{\prime \prime } = y^{2} \left (a x +b y\right )+{y^{\prime }}^{2}
\]
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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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| \[
{} 2 y y^{\prime \prime } = 8 y^{3}-2 y^{2} \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )-3 f \left (x \right ) y y^{\prime }+{y^{\prime }}^{2}
\]
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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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| \[
{} 2 y y^{\prime \prime } = f \left (x \right ) y^{2}+3 {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = y \left (\operatorname {a2} +\operatorname {a3} y^{2}\right )+x \left (\operatorname {a0} +\operatorname {a1} y^{4}\right )-y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} x y y^{\prime \prime } = b^{2} x y^{3}+a y y^{\prime }+x {y^{\prime }}^{2}
\]
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| \[
{} \operatorname {f3} \left (x \right ) y^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f0} \left (x \right ) y y^{\prime \prime } = 0
\]
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| \[
{} 4 f \left (x \right ) y y^{\prime \prime } = 4 f \left (x \right )^{2} y+3 f \left (x \right ) g \left (x \right ) y^{2}-f \left (x \right ) y^{4}+2 y^{3} f^{\prime }\left (x \right )+\left (-6 f \left (x \right ) y^{2}+2 f^{\prime }\left (x \right )\right ) y^{\prime }+3 f \left (x \right ) {y^{\prime }}^{2}
\]
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| \[
{} y {y^{\prime }}^{2}+y^{2} y^{\prime \prime } = b x +a
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
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| \[
{} \left (x^{2}+y^{2}\right ) y^{\prime \prime } = 2 \left (1+y^{2}\right ) \left (x y^{\prime }-y\right )
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = 4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-y\right ) y y^{\prime \prime } = -\left (1-y\right )^{3} \left (\operatorname {F0} \left (x \right )^{2}-\operatorname {G0} \left (x \right )^{2} y^{2}\right )-4 \left (1-y\right ) y^{2} \left (f \left (x \right )^{2}-g \left (x \right )^{2}+f^{\prime }\left (x \right )+g^{\prime }\left (x \right )\right )-4 y \left (f \left (x \right )+g \left (x \right ) y\right ) y^{\prime }+\left (1-3 y\right ) {y^{\prime }}^{2}
\]
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| \[
{} \operatorname {a2} x \left (1-y\right ) y^{2}+\operatorname {a3} \,x^{3} y^{2} \left (1+y\right )+\left (1-y\right )^{3} \left (\operatorname {a0} +\operatorname {a1} y^{2}\right )+2 x \left (1-y\right ) y y^{\prime }-x^{2} \left (1-3 y\right ) {y^{\prime }}^{2}+2 x^{2} \left (1-y\right ) y y^{\prime \prime } = 0
\]
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| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = -y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-x \right ) x \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = f \left (x \right ) \left (\left (1-y\right ) \left (x -y\right ) y\right )^{{3}/{2}}-y^{2} \left (1-y^{2}\right )+2 \left (1-y\right ) y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right ) x \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} 2 \left (1-x \right )^{2} x^{2} \left (1-y\right ) \left (x -y\right ) y y^{\prime \prime } = \operatorname {a0} x \left (1-y\right )^{2} \left (x -y\right )^{2}+\left (\operatorname {a2} -1\right ) \left (1-x \right ) x \left (1-y\right )^{2} y^{2}+\operatorname {a1} \left (1-x \right ) \left (x -y\right )^{2} y^{2}+\operatorname {a3} \left (1-y\right )^{2} \left (x -y\right )^{2} y^{2}+2 \left (1-x \right ) x \left (1-y\right )^{2} y \left (x^{2}+y-2 x y\right ) y^{\prime }+\left (1-x \right )^{2} x^{2} \left (x -2 y-2 x y+3 y^{2}\right ) {y^{\prime }}^{2}
\]
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| \[
{} \operatorname {f3} \left (y\right )+\operatorname {f2} \left (y\right ) y^{\prime }+\operatorname {f1} \left (y\right ) {y^{\prime }}^{2}+\operatorname {f0} \left (y\right ) y^{\prime \prime } = 0
\]
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| \[
{} X \left (x , y\right )^{3} y^{\prime \prime } = 1
\]
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| \[
{} y^{\prime } y^{\prime \prime } = x y^{2}+x^{2} y y^{\prime }
\]
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| \[
{} y+x y^{\prime }+2 \left (x +y\right ) {y^{\prime }}^{2}+\left (y^{2}+2 x^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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| \[
{} y+3 x y^{\prime }+2 {y^{\prime }}^{3} y+\left (x^{2}+2 y^{2} y^{\prime }\right ) y^{\prime \prime } = 0
\]
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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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| \[
{} 2 \left (x -y^{\prime }\right ) y^{\prime }-x \left (x +4 y^{\prime }\right ) y^{\prime \prime }+2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2} = 2 y
\]
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| \[
{} f^{\prime }\left (x \right ) y+2 f \left (x \right ) y^{\prime }+y^{\prime \prime \prime } = 0
\]
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| \[
{} 2 y \left (2 f \left (x \right ) g \left (x \right )+g^{\prime }\left (x \right )\right )+\left (4 g \left (x \right )+f^{\prime }\left (x \right )+2 {f^{\prime }\left (x \right )}^{2}\right ) y^{\prime }+3 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
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| \[
{} 2 x^{3} y+\left (-2 x^{3}+6\right ) y^{\prime }+x \left (-x^{2}+6\right ) y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = 0
\]
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| \[
{} -6 y+6 y^{\prime } \left (1+x \right )-3 x \left (x +2\right ) y^{\prime \prime }+x^{2} \left (3+y\right ) y^{\prime \prime \prime } = 0
\]
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| \[
{} 10 f^{\prime }\left (x \right ) y^{\prime }+3 y \left (3 f \left (x \right )^{2}+f^{\prime \prime }\left (x \right )\right )+10 f \left (x \right ) y^{\prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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| \[
{} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = 0
\]
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| \[
{} y^{2}-2 y^{\prime \prime \prime }+y^{\prime \prime \prime \prime } = x^{3}
\]
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| \[
{} -y y^{\prime }+{y^{\prime }}^{2}+y^{\prime \prime \prime } = 0
\]
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| \[
{} a y y^{\prime \prime }+y^{\prime \prime \prime } = 0
\]
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| \[
{} y^{2}-\left (1-2 x y\right ) y^{\prime }+x y^{\prime \prime }+x^{2} y^{\prime \prime \prime } = f \left (x \right )
\]
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| \[
{} y^{\prime } y^{\prime \prime } = a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2}
\]
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| \[
{} \frac {x^{n} y^{\prime }}{b y^{2}-c \,x^{2 a}}-\frac {a y x^{a -1}}{b y^{2}-c \,x^{2 a}}+x^{a -1} = 0
\]
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| \[
{} s^{2}+s^{\prime } = \frac {s+1}{s t}
\]
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| \[
{} x^{\prime }+t x = {\mathrm e}^{x}
\]
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| \[
{} x x^{\prime }+x t^{2} = \sin \left (t \right )
\]
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| \[
{} 1+\frac {1}{1+x^{2}+4 x y+y^{2}}+\left (\frac {1}{\sqrt {y}}+\frac {1}{1+x^{2}+2 x y+y^{2}}\right ) y^{\prime } = 0
\]
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| \[
{} y^{\prime \prime }+y = 0
\]
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| \[
{} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y = 0
\]
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| \[
{} u^{\prime \prime }+u^{\prime }+u = \cos \left (r +u\right )
\]
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| \[
{} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x = 0
\]
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| \[
{} \sin \left (x^{\prime }\right )+y^{3} x = \sin \left (y \right )
\]
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| \[
{} y^{\prime \prime }+4 y = 0
\]
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| \[
{} y^{\prime \prime }+4 y = 0
\]
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| \[
{} y^{\prime } = 6 \sqrt {y}+5 x^{3}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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| \[
{} y^{\prime } = {\mathrm e}^{-\frac {x y^{2}}{100}}
\]
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| \[
{} x y^{\prime }-4 y = x^{6} {\mathrm e}^{x}
\]
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| \[
{} y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0
\]
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| \[
{} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\]
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| \[
{} [y_{1}^{\prime }\left (x \right ) = 3 y_{1} \left (x \right )+x y_{3} \left (x \right ), y_{2}^{\prime }\left (x \right ) = y_{2} \left (x \right )+x^{3} y_{3} \left (x \right ), y_{3}^{\prime }\left (x \right ) = 2 y_{1} \left (x \right ) x -y_{2} \left (x \right )+{\mathrm e}^{x} y_{3} \left (x \right )]
\]
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| \[
{} 2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime }
\]
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| \[
{} [x^{\prime }\left (t \right ) = x \left (t \right ) y \left (t \right )+1, y^{\prime }\left (t \right ) = -x \left (t \right )+y \left (t \right )]
\]
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{} [x^{\prime }\left (t \right ) = 1+t y \left (t \right ), y^{\prime }\left (t \right ) = -t x \left (t \right )+y \left (t \right )]
\]
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| \[
{} y^{\prime } = y+x \,{\mathrm e}^{y}
\]
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| \[
{} y^{\prime \prime }+5 x y^{\prime }+y \sqrt {x} = 0
\]
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{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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{} 2 y^{\prime \prime } = \sin \left (2 y\right )
\]
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{} y^{\prime } = \sqrt {-y^{2}-x^{2}+1}
\]
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| \[
{} y y^{\prime \prime } = x
\]
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{} 3 y y^{\prime \prime } = \sin \left (x \right )
\]
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| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{3} = 0
\]
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| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x y-x^{3}-x^{2} = 0
\]
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| \[
{} y^{\prime \prime }-x^{3} y^{\prime }-x^{3} y-x^{4}-x^{3} = 0
\]
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