| # | ODE | Mathematica | Maple | Sympy |
| \[
{} y^{\prime }+y^{2}-a x -b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+y^{2}+a \,x^{m} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+y^{2}+\left (x y-1\right ) f \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y^{2}-x y-x +1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y^{2}+\sin \left (x \right ) y-\cos \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+a y^{2}-b \,x^{\nu } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+a y \left (y-x \right )-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+x^{-a -1} y^{2}-x^{a} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+\sin \left (x \right ) y^{2}-\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+y^{3}+a x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+3 a y^{3}+6 a x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-x \left (x +2\right ) y^{3}-\left (x +3\right ) y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+\left (4 a^{2} x +3 x^{2} a +b \right ) y^{3}+3 x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {f \left (x \right ) a +b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-a y^{n}-b \,x^{\frac {n}{-n +1}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-a^{n} f \left (x \right )^{-n +1} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-a \sqrt {y}-b x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\frac {y-x^{2} \sqrt {x^{2}-y^{2}}}{x y \sqrt {x^{2}-y^{2}}+x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{x^{2} a +b x +c}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-a \cos \left (y\right )+b = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y^{\prime }-\tan \left (x y\right ) = 0
\]
|
✗ |
✓ |
✗ |
|
| \[
{} y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+x^{2}+y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a y^{2}-y+b \,x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a y^{2}-b y+c \,x^{2 b} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a y^{2}-b y-c \,x^{\beta } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a +x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+x y^{2}-y-a \,x^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a x y^{2}+2 y+b x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a x y^{2}+b y+c x +d = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+f \left (x \right ) \left (-x^{2}+y^{2}\right )-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+y^{3}+3 x y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-x \left (y-x \right ) \sqrt {x^{2}+y^{2}}-y = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-\sin \left (x -y\right ) = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }-y f \left (x^{a} y^{b}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 x y-1\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2}-1\right ) y^{\prime }+a \left (1-2 x y+y^{2}\right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y^{\prime }-2 y^{2}-x y+2 a^{2} x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x^{2} y^{\prime }-2 y^{2}-3 x y+2 a^{2} x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y^{2}-x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2} a +b x +c \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{7} y^{\prime }+5 y^{2} x^{3}+2 \left (x^{2}+1\right ) y^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (1+m \right )} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} x \ln \left (x \right ) y^{\prime }-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y^{\prime } \sin \left (x \right )-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} \left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} 2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }+x^{3}+y = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+a y+x = 0
\]
|
✓ |
✓ |
✗ |
|
| \[
{} y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0
\]
|
✗ |
✗ |
✗ |
|
| \[
{} y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0
\]
|
✓ |
✓ |
✗ |
|