| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y y^{\prime }-y = -\frac {2 \left (1+m \right )}{\left (3+m \right )^{2}}+A \,x^{m}
\]
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| \[
{} y y^{\prime }-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (3+m \right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (3+m \right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}}
\]
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| \[
{} y y^{\prime }-y = \frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}}
\]
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| \[
{} y y^{\prime }-y = -\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4}
\]
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| \[
{} y y^{\prime }-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25}
\]
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| \[
{} y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98}
\]
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| \[
{} y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{{7}/{5}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242}
\]
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| \[
{} y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (n +1\right ) \left (3+n \right ) A^{2}}{\sqrt {x}}\right )
\]
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| \[
{} y y^{\prime }-y = A \left (n +2\right ) \left (\sqrt {x}+2 \left (n +2\right ) A +\frac {\left (3+2 n \right ) A^{2}}{\sqrt {x}}\right )
\]
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| \[
{} y y^{\prime }-y = A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}}
\]
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| \[
{} y y^{\prime }-y = 2 A^{2}-A \sqrt {x}
\]
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| \[
{} y y^{\prime }-y = -\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25}
\]
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| \[
{} y y^{\prime }-y = -\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = \frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}}
\]
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| \[
{} y y^{\prime }-y = \frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}}
\]
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| \[
{} y y^{\prime }-y = 12 x +\frac {A}{x^{{5}/{2}}}
\]
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| \[
{} y y^{\prime }-y = \frac {63 x}{4}+\frac {A}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right )
\]
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| \[
{} y y^{\prime }-y = 2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right )
\]
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| \[
{} y y^{\prime }-y = -\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+A \sqrt {x}
\]
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| \[
{} y y^{\prime }-y = 20 x +\frac {A}{\sqrt {x}}
\]
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| \[
{} y y^{\prime }-y = \frac {15 x}{4}+\frac {A}{x^{7}}
\]
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| \[
{} y y^{\prime }-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49}
\]
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| \[
{} y y^{\prime }-y = -\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50}
\]
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| \[
{} y y^{\prime }-y = \frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{{3}/{5}}}-\frac {B}{x^{{7}/{5}}}
\]
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| \[
{} y y^{\prime }-y = \frac {k}{\sqrt {A \,x^{2}+B x +c}}
\]
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| \[
{} y y^{\prime }-y = -\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}}
\]
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| \[
{} y y^{\prime }-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (-A +2\right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75}
\]
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| \[
{} y y^{\prime }-y = \frac {3 x}{4}-\frac {3 A \,x^{{1}/{3}}}{2}+\frac {3 A^{2}}{4 x^{{1}/{3}}}-\frac {27 A^{4}}{625 x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {6 x}{25}+\frac {7 A \,x^{{1}/{3}}}{5}+\frac {31 A^{2}}{3 x^{{1}/{3}}}-\frac {100 A^{4}}{3 x^{{5}/{3}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{{1}/{5}}}-\frac {7 A^{3}}{20 x^{{4}/{5}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{{5}/{11}}}-\frac {770 A^{3}}{9 x^{{13}/{11}}}
\]
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| \[
{} y y^{\prime }-y = -\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{{1}/{7}}}+\frac {280 A}{x^{{5}/{7}}}-\frac {400 A^{2}}{x^{{9}/{7}}}\right )}{9}
\]
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| \[
{} y y^{\prime }-y = a x +b \,x^{m}
\]
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| \[
{} y y^{\prime }-y = -\frac {\left (1+m \right ) x}{\left (m +2\right )^{2}}+A \,x^{2 m +1}+B \,x^{3 m +1}
\]
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| \[
{} y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b
\]
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| \[
{} y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}+a \lambda x \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\lambda x}
\]
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| \[
{} y y^{\prime }-y = 2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 \sin \left (\lambda x \right ) a
\]
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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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| \[
{} y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1
\]
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| \[
{} y y^{\prime } = \left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1
\]
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| \[
{} y y^{\prime } = \left ({\mathrm e}^{\lambda x} a +b \,{\mathrm e}^{-\lambda x}\right ) y+1
\]
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| \[
{} y y^{\prime } = a y \cosh \left (x \right )+1
\]
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| \[
{} y y^{\prime } = a y \sinh \left (x \right )+1
\]
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| \[
{} y y^{\prime } = a \cos \left (\lambda x \right ) y+1
\]
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| \[
{} y y^{\prime } = a \sin \left (\lambda x \right ) y+1
\]
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| \[
{} y y^{\prime } = \left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x
\]
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| \[
{} 2 y y^{\prime } = \left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x
\]
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| \[
{} y y^{\prime } = \left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x
\]
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| \[
{} y y^{\prime } = x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right )
\]
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| \[
{} y y^{\prime } = \left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y+\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{-1+2 n}
\]
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| \[
{} y y^{\prime } = \left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x}
\]
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| \[
{} y y^{\prime } = \frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}+\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L}
\]
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| \[
{} y y^{\prime } = \left (a \left (2 n +1\right ) x^{2}+c x +b \left (-1+2 n \right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3}
\]
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| \[
{} y y^{\prime } = \left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3}
\]
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| \[
{} y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x}
\]
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| \[
{} 3 y y^{\prime } = \frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{{1}/{3}}}+\frac {6 \lambda s x -6}{x^{{2}/{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{{1}/{3}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x}
\]
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| \[
{} y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2} = \frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}
\]
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| \[
{} y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x -8\right )}{14 x^{{11}/{17}}}
\]
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| \[
{} y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{{11}/{17}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{{23}/{13}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}} = -\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}} = a^{2} \left (-x^{2}+1\right )
\]
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| \[
{} y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35} = -\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{{9}/{5}}}{35}
\]
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| \[
{} y y^{\prime }+\frac {3 a \left (3 x +7\right ) y}{10 x^{{13}/{10}}} = -\frac {a^{2} \left (x -1\right ) \left (9+x \right )}{5 x^{{8}/{5}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}}
\]
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| \[
{} y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}}
\]
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| \[
{} y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{{13}/{7}}}
\]
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| \[
{} y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (5+3 x \right )}{4 x^{{5}/{2}}}
\]
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| \[
{} y y^{\prime }-\frac {a \left (1+x \right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x +5\right )}{4 x^{{5}/{2}}}
\]
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| \[
{} y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}} = -\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}}
\]
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| \[
{} y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{{8}/{7}}} = \frac {a^{2} \left (x -1\right ) \left (32 x +3\right )}{28 x^{{9}/{7}}}
\]
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| \[
{} y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}
\]
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| \[
{} y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}} = \frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}}
\]
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| \[
{} y y^{\prime }+\frac {a \left (x -2\right ) y}{x} = \frac {2 a^{2} \left (x -1\right )}{x}
\]
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| \[
{} y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x} = -\frac {2 a^{2} \left (x -1\right )^{2}}{x}
\]
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| \[
{} y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x} = \frac {a^{2} b}{x}
\]
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|
| \[
{} y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}}
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}} = -\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}}
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{{22}/{15}}} = -\frac {a^{2} \left (x -1\right ) \left (x +4\right )}{30 x^{{29}/{15}}}
\]
|
✗ |
✗ |
✗ |
|