| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=-2 x \left (y^{3}-3 y+2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.102 |
|
| \begin{align*}
y^{\prime }+x^{2} \left (1+y\right ) \left (y-2\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.762 |
|
| \begin{align*}
y^{\prime }&=\left (a +b x y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.759 |
|
| \begin{align*}
a y^{3} x +b y^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
4.859 |
|
| \begin{align*}
y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
5.466 |
|
| \begin{align*}
y^{\prime }+x \left (x +y\right )&=x^{3} \left (x +y\right )^{3}-1 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✓ |
3.737 |
|
| \begin{align*}
a y^{3} x +b y^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.662 |
|
| \begin{align*}
y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
4.196 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 b x}+y^{3} {\mathrm e}^{-3 b x}\right ) {\mathrm e}^{b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.986 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-\frac {4 x}{3}}+y^{3} {\mathrm e}^{-2 x}\right ) {\mathrm e}^{\frac {2 x}{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.474 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{-2 x}+y^{3} {\mathrm e}^{-3 x}\right ) {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
6.556 |
|
| \begin{align*}
y^{\prime }&=\left (1+y^{2} {\mathrm e}^{2 x^{2}}+y^{3} {\mathrm e}^{3 x^{2}}\right ) {\mathrm e}^{-x^{2}} x \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
8.999 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +x^{3}+x y^{2}+y^{3}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
5.904 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{3} y+x^{6}+y^{2} x^{2}+y^{3}}{x^{4}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.108 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2} y+1+x^{6} y^{2}+y^{3} x^{9}}{x^{3}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.586 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} y+x^{3}+x y^{2}+y^{3}}{\left (x -1\right ) x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
14.750 |
|
| \begin{align*}
y^{\prime }&=\frac {-b^{3}+6 b^{2} x -12 b \,x^{2}+8 x^{3}-4 b y^{2}+8 x y^{2}+8 y^{3}}{\left (2 x -b \right )^{3}} \\
\end{align*} | [[_homogeneous, ‘class C‘], _rational, _Abel] | ✓ | ✓ | ✓ | ✗ | 38.385 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y \,{\mathrm e}^{-\frac {x^{2}}{4}} x +2+2 y^{2} {\mathrm e}^{-\frac {x^{2}}{2}}+2 y^{3} {\mathrm e}^{-\frac {3 x^{2}}{4}}\right ) {\mathrm e}^{\frac {x^{2}}{4}}}{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
15.151 |
|
| \begin{align*}
y^{\prime }&=\frac {b^{3}+y^{2} b^{3}+2 a \,b^{2} x y+a^{2} b \,x^{2}+b^{3} y^{3}+3 a \,b^{2} x y^{2}+3 a^{2} b \,x^{2} y+a^{3} x^{3}}{b^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
36.129 |
|
| \begin{align*}
y^{\prime }&=\frac {\alpha ^{3}+y^{2} \alpha ^{3}+2 y \alpha ^{2} \beta x +\alpha \,\beta ^{2} x^{2}+y^{3} \alpha ^{3}+3 y^{2} \alpha ^{2} \beta x +3 y \alpha \,\beta ^{2} x^{2}+\beta ^{3} x^{3}}{\alpha ^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
36.254 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{3}+y^{2} a^{3}+2 a^{2} b x y+b^{2} x^{2} a +y^{3} a^{3}+3 a^{2} b x y^{2}+3 a \,b^{2} x^{2} y+b^{3} x^{3}}{a^{3}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
36.102 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x}{3}+1+y^{2}+\frac {2 x^{2} y}{3}+\frac {x^{4}}{9}+y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
5.194 |
|
| \begin{align*}
y^{\prime }&=2 x +1+y^{2}-2 x^{2} y+x^{4}+y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.191 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-256 a \,x^{2}+512+512 y^{2}+128 y a \,x^{4}+8 a^{2} x^{8}+512 y^{3}+192 x^{4} a y^{2}+24 y a^{2} x^{8}+a^{3} x^{12}\right ) x}{512} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
7.204 |
|
| \begin{align*}
y^{\prime }&=-\frac {\left (-108 x^{{3}/{2}}-216-216 y^{2}+72 x^{3} y-6 x^{6}-216 y^{3}+108 x^{3} y^{2}-18 x^{6} y+x^{9}\right ) \sqrt {x}}{216} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.036 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x^{2}-4 x^{3} y+1+x^{4} y^{2}+x^{6} y^{3}-3 x^{5} y^{2}+3 x^{4} y-x^{3}}{x^{4}} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
12.159 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x +x^{3}+x^{3} y^{2}+4 x^{2} y+x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8}{x^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.201 |
|
| \begin{align*}
y^{\prime }&=\frac {32 x^{5}+64 x^{6}+64 x^{6} y^{2}+32 x^{4} y+4 x^{2}+64 x^{6} y^{3}+48 x^{4} y^{2}+12 x^{2} y+1}{64 x^{8}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.805 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{2} x +a^{3} x^{3}+a^{3} x^{3} y^{2}+2 y a^{2} x^{2}+a x +a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1}{a^{3} x^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
6.833 |
|
| \begin{align*}
y^{\prime }&=\frac {-2 x -y+1+y^{2} x^{2}+2 x^{3} y+x^{4}+x^{3} y^{3}+3 x^{4} y^{2}+3 x^{5} y+x^{6}}{x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
5.314 |
|
| \begin{align*}
y^{\prime }&=-\frac {x \left ({\mathrm e}^{-3 x^{2}} x^{6}-6 \,{\mathrm e}^{-2 x^{2}} x^{4} y-2 \,{\mathrm e}^{-2 x^{2}} x^{4}+12 x^{2} {\mathrm e}^{-x^{2}} y^{2}+8 x^{2} {\mathrm e}^{-x^{2}} y+8 x^{2} {\mathrm e}^{-x^{2}}-8 y^{3}-8 y^{2}-8 \,{\mathrm e}^{-x^{2}}-8\right )}{8} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
9.009 |
|
| \begin{align*}
y^{\prime }&=-\frac {-x^{2}-y x -x^{3}-x y^{2}+2 y \ln \left (x \right ) x^{2}-x^{3} \ln \left (x \right )^{2}-y^{3}+3 x y^{2} \ln \left (x \right )-3 x^{2} \ln \left (x \right )^{2} y+x^{3} \ln \left (x \right )^{3}}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
8.328 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{4}-y x -\frac {x^{4}}{8}+\frac {x^{3}}{8}+\frac {x^{2}}{4}+y^{3}-\frac {3 y^{2} x^{2}}{4}-\frac {3 x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 x^{3} y}{4}-\frac {x^{6}}{64}-\frac {3 x^{5}}{32} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Abel] | ✓ | ✓ | ✓ | ✗ | 8.226 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {7 x^{2} y}{2}-2 y x +\frac {13 x^{4}}{16}-\frac {3 x^{3}}{2}+x^{2}+y^{3}+\frac {3 y^{2} x^{2}}{4}-3 x y^{2}+\frac {3 x^{4} y}{16}-\frac {3 x^{3} y}{2}+\frac {x^{6}}{64}-\frac {3 x^{5}}{16} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
12.688 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4}+1+y^{2}+\frac {7 x^{2} y}{16}-\frac {y x}{2}+\frac {5 x^{4}}{128}-\frac {5 x^{3}}{64}+\frac {x^{2}}{16}+y^{3}+\frac {3 y^{2} x^{2}}{8}-\frac {3 x y^{2}}{4}+\frac {3 x^{4} y}{64}-\frac {3 x^{3} y}{16}+\frac {x^{6}}{512}-\frac {3 x^{5}}{256} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.829 |
|
| \begin{align*}
y^{\prime }&=\frac {-x^{2}+x +1+y^{2}+5 x^{2} y-2 y x +4 x^{4}-3 x^{3}+y^{3}+3 y^{2} x^{2}-3 x y^{2}+3 x^{4} y-6 x^{3} y+x^{6}-3 x^{5}}{x} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
9.148 |
|
| \begin{align*}
y^{\prime }&=-\frac {a x}{2}+1+y^{2}+\frac {a \,x^{2} y}{2}+b x y+\frac {a^{2} x^{4}}{16}+\frac {a \,x^{3} b}{4}+\frac {b^{2} x^{2}}{4}+y^{3}+\frac {3 a \,x^{2} y^{2}}{4}+\frac {3 b x y^{2}}{2}+\frac {3 a^{2} x^{4} y}{16}+\frac {3 y a \,x^{3} b}{4}+\frac {3 b^{2} x^{2} y}{4}+\frac {a^{3} x^{6}}{64}+\frac {3 a^{2} x^{5} b}{32}+\frac {3 a \,x^{4} b^{2}}{16}+\frac {b^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.408 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{2}+1+y^{2}+\frac {x^{2} y}{2}+a x y+\frac {x^{4}}{16}+\frac {a \,x^{3}}{4}+\frac {a^{2} x^{2}}{4}+y^{3}+\frac {3 y^{2} x^{2}}{4}+\frac {3 a x y^{2}}{2}+\frac {3 x^{4} y}{16}+\frac {3 y a \,x^{3}}{4}+\frac {3 y a^{2} x^{2}}{4}+\frac {x^{6}}{64}+\frac {3 x^{5} a}{32}+\frac {3 a^{2} x^{4}}{16}+\frac {a^{3} x^{3}}{8} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.365 |
|
| \begin{align*}
y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 \sqrt {x}\, y+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 x^{6} y+600 y x^{{7}/{2}}+1500 y x -8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
13.138 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +4 y \ln \left (2 x +1\right ) x +6 y^{2} \ln \left (2 x +1\right ) x +6 y \ln \left (2 x +1\right )^{2} x +2 \ln \left (2 x +1\right )^{3} x +2 x y^{3}+2 \ln \left (2 x +1\right )^{2} x +2 x y^{2}-1+3 y^{2} \ln \left (2 x +1\right )+3 y \ln \left (2 x +1\right )^{2}+y^{2}+y^{3}+2 y \ln \left (2 x +1\right )+\ln \left (2 x +1\right )^{2}+\ln \left (2 x +1\right )^{3}}{2 x +1} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.328 |
|
| \begin{align*}
y^{\prime }&=\frac {-4 \cos \left (x \right ) x +4 x^{2} \sin \left (x \right )+4 x +4+4 y^{2}+8 y \cos \left (x \right ) x -8 y x +2 \cos \left (2 x \right ) x^{2}+6 x^{2}-8 x^{2} \cos \left (x \right )+4 y^{3}+12 y^{2} \cos \left (x \right ) x -12 x y^{2}+6 y x^{2} \cos \left (2 x \right )+18 x^{2} y-24 y \cos \left (x \right ) x^{2}+x^{3} \cos \left (3 x \right )+15 \cos \left (x \right ) x^{3}-6 x^{3} \cos \left (2 x \right )-10 x^{3}}{4 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
13.539 |
|
| \begin{align*}
y^{\prime }&=-\frac {x \left (-513-432 x -576 x^{5}-594 x^{2} y-1134 x^{2}-972 x^{4} y^{2}-378 y+864 x^{5} y^{2}-864 x^{4}-216 x^{4} y-456 x^{6}+288 x^{7} y-144 x^{7}+720 x^{3} y-96 x^{8}-1296 y^{2} x^{2}-216 y^{3}-288 x^{6} y-216 x^{6} y^{3}-288 y x^{8}-756 x^{3}+432 x^{3} y^{2}-540 y^{2}-648 x^{2} y^{3}+1008 x^{5} y+64 x^{9}-648 y^{3} x^{4}-216 x^{6} y^{2}+432 y^{2} x^{7}\right )}{216 \left (x^{2}+1\right )^{4}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
8.628 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right )^{3}}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
35.019 |
|
| \begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{b x}+{\mathrm e}^{2 b x}\right ) {\mathrm e}^{-2 b x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
10.626 |
|
| \begin{align*}
y^{\prime }&=y^{3}-3 y^{2} x^{2}+3 x^{4} y-x^{6}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
7.892 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y^{2} x^{2}+\frac {x^{4} y}{3}+\frac {x^{6}}{27}-\frac {2 x}{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
8.181 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2} x^{7}+x^{4} y+x -3\right )}{x} \\
\end{align*} | [_rational, _Abel] | ✓ | ✓ | ✓ | ✓ | 15.837 |
|
| \begin{align*}
y^{\prime }&=y \left (y^{2}+y \,{\mathrm e}^{-x^{2}}+{\mathrm e}^{-2 x^{2}}\right ) {\mathrm e}^{2 x^{2}} x \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
15.355 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (y^{2}+y x +x^{2}+x \right )}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
13.324 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x}{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Abel] |
✓ |
✓ |
✓ |
✓ |
10.452 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3} y^{3}+6 y^{2} x^{2}+12 y x +8+2 x}{x^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
9.788 |
|
| \begin{align*}
y^{\prime }&=\frac {a^{3} x^{3} y^{3}+3 y^{2} a^{2} x^{2}+3 a x y+1+a^{2} x}{x^{3} a^{3}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
10.708 |
|
| \begin{align*}
y^{\prime }&=\frac {y \,{\mathrm e}^{-\frac {x^{2}}{2}} \left (2 y^{2}+2 y \,{\mathrm e}^{\frac {x^{2}}{4}}+2 \,{\mathrm e}^{\frac {x^{2}}{2}}+x \,{\mathrm e}^{\frac {x^{2}}{2}}\right )}{2} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
66.949 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2}+3 x^{2} y-x^{3}+x^{2}}{\left (x -1\right ) \left (x +1\right )} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
16.802 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y x +1\right ) \left (y^{2} x^{2}+x^{2} y+2 y x +1+x +x^{2}\right )}{x^{5}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
8.763 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-3 x y^{2} \ln \left (x \right )+3 x^{2} \ln \left (x \right )^{2} y-x^{3} \ln \left (x \right )^{3}+x^{2}+y x}{x^{2}} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
8.497 |
|
| \begin{align*}
y^{\prime }&=-y^{3}+\frac {y^{2}}{\sqrt {a x +b}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
15.069 |
|
| \begin{align*}
y^{\prime }&=a y^{3}+3 a b x y^{2}-b -2 a \,b^{3} x^{3} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
4.201 |
|
| \begin{align*}
y^{\prime }&=a y^{3} x +b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
6.846 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}-b m \,x^{m -1}-2 a \,b^{3} x^{n +3 m} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
7.417 |
|
| \begin{align*}
y^{\prime }&=a \,x^{n} y^{3}+3 a b \,x^{n +m} y^{2}+c \,x^{k} y-2 a \,b^{3} x^{n +3 m}+b c \,x^{m +k}-b m \,x^{m -1} \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
13.229 |
|
| \begin{align*}
y^{\prime } x&=a y^{3}+3 a b \,x^{n} y^{2}-b n \,x^{n}-2 a \,b^{3} x^{3 n} \\
\end{align*} |
[_rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.759 |
|
| \begin{align*}
y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Abel] | ✓ | ✓ | ✓ | ✓ | 5.053 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{2 \lambda x} y^{3}+b \,{\mathrm e}^{\lambda x} y^{2}+c y+d \,{\mathrm e}^{-\lambda x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✗ |
5.546 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{\lambda x} y^{2}+c y-2 a \,b^{3} {\mathrm e}^{\lambda x}+b c \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
6.297 |
|
| \begin{align*}
y^{\prime }&=a \,{\mathrm e}^{\lambda x} y^{3}+3 a b \,{\mathrm e}^{x \left (\lambda +\mu \right )} y^{2}-2 a \,b^{3} {\mathrm e}^{\left (\lambda +3 \mu \right ) x}-{\mathrm e}^{\mu x} b \mu \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
5.313 |
|