|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } y = \frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}+\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
15.151 |
|
|
\[
{}y^{\prime } y = \left (a \left (2 n +1\right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.897 |
|
|
\[
{}y^{\prime } y = \left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
34.583 |
|
|
\[
{}y^{\prime } y-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.378 |
|
|
\[
{}y^{\prime } y-a \left (1-\frac {b}{\sqrt {x}}\right ) y = \frac {a^{2} b}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.337 |
|
|
\[
{}y^{\prime } y = \frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.813 |
|
|
\[
{}3 y^{\prime } y = \frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{{1}/{3}}}+\frac {6 \lambda s x -6}{x^{{2}/{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{{1}/{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
19.862 |
|
|
\[
{}y^{\prime } y+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.217 |
|
|
\[
{}y^{\prime } y-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2} = \frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.739 |
|
|
\[
{}y^{\prime } y+\frac {a \left (13 x -20\right ) y}{14 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x -8\right )}{14 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
84.489 |
|
|
\[
{}y^{\prime } y+\frac {5 a \left (23 x -16\right ) y}{56 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
91.959 |
|
|
\[
{}y^{\prime } y+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{{23}/{13}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
23.843 |
|
|
\[
{}y^{\prime } y+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}} = -\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.249 |
|
|
\[
{}y^{\prime } y+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}} = a^{2} \left (-x^{2}+1\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.259 |
|
|
\[
{}y^{\prime } y+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35} = -\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{{9}/{5}}}{35}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.506 |
|
|
\[
{}y^{\prime } y+\frac {3 a \left (3 x +7\right ) y}{10 x^{{13}/{10}}} = -\frac {a^{2} \left (x -1\right ) \left (x +9\right )}{5 x^{{8}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
80.440 |
|
|
\[
{}y^{\prime } y+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.437 |
|
|
\[
{}y^{\prime } y+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.586 |
|
|
\[
{}y^{\prime } y+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{{13}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.427 |
|
|
\[
{}y^{\prime } y-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
25.180 |
|
|
\[
{}y^{\prime } y-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
23.794 |
|
|
\[
{}y^{\prime } y-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.784 |
|
|
\[
{}y^{\prime } y+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}} = -\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
12.622 |
|
|
\[
{}y^{\prime } y-\frac {a \left (8 x -1\right ) y}{28 x^{{8}/{7}}} = \frac {a^{2} \left (x -1\right ) \left (32 x +3\right )}{28 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.237 |
|
|
\[
{}y^{\prime } y-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.707 |
|
|
\[
{}y^{\prime } y-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}} = \frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.743 |
|
|
\[
{}y^{\prime } y+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.045 |
|
|
\[
{}y^{\prime } y+\frac {a \left (-2+x \right ) y}{x} = \frac {2 a^{2} \left (x -1\right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.128 |
|
|
\[
{}y^{\prime } y+\frac {a \left (3 x -2\right ) y}{x} = -\frac {2 a^{2} \left (x -1\right )^{2}}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.704 |
|
|
\[
{}y^{\prime } y+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x} = \frac {a^{2} b}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.484 |
|
|
\[
{}y^{\prime } y-\frac {a \left (-4+3 x \right ) y}{4 x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.293 |
|
|
\[
{}y^{\prime } y+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.414 |
|
|
\[
{}y^{\prime } y-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}} = -\frac {a^{2} \left (x -1\right ) \left (-4+3 x \right )}{8 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.373 |
|
|
\[
{}y^{\prime } y+\frac {a \left (17 x +18\right ) y}{30 x^{{22}/{15}}} = -\frac {a^{2} \left (x -1\right ) \left (4+x \right )}{30 x^{{29}/{15}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
76.484 |
|
|
\[
{}y^{\prime } y-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}} = -\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.567 |
|
|
\[
{}y^{\prime } y+\frac {a \left (24 x +11\right ) x^{{27}/{20}} y}{30} = -\frac {a^{2} \left (x -1\right ) \left (9 x +1\right )}{60 x^{{17}/{10}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
107.542 |
|
|
\[
{}y^{\prime } y-\frac {2 a \left (2+3 x \right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.669 |
|
|
\[
{}y^{\prime } y-\frac {6 a \left (1+4 x \right ) y}{5 x^{{7}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.375 |
|
|
\[
{}y^{\prime } y-\frac {a \left (4+x \right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.353 |
|
|
\[
{}y^{\prime } y-\frac {a \left (4+x \right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.872 |
|
|
\[
{}y^{\prime } y-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +1\right )}{2 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.358 |
|
|
\[
{}y^{\prime } y+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}} = \frac {2 a^{2} \left (x -1\right ) \left (4+x \right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.424 |
|
|
\[
{}y^{\prime } y+\frac {a \left (21 x +19\right ) y}{5 x^{{7}/{5}}} = -\frac {2 a^{2} \left (x -1\right ) \left (9 x -4\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
39.488 |
|
|
\[
{}y^{\prime } y-\frac {3 a y}{x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
12.368 |
|
|
\[
{}y^{\prime } y-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (k +1\right ) \left (x -1\right )}{x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.628 |
|
|
\[
{}y^{\prime } y-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (x -1\right )^{2} x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.425 |
|
|
\[
{}y^{\prime } y-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2} = \frac {a^{2} \left (2 k -3\right ) \left (x -1\right )^{2} x^{1-2 k}}{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.055 |
|
|
\[
{}y^{\prime } y-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y = n \left (x -a \right ) x^{-2 n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.980 |
|
|
\[
{}y^{\prime } y-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y = n \,x^{2 n} \left (x -a \right )^{-2 n -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
10.602 |
|
|
\[
{}y^{\prime } y-a \left (\left (2 k -3\right ) x +1\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{2-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.471 |
|
|
\[
{}y^{\prime } y-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y = a^{2} \left (\left (n +k -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
9.278 |
|
|
\[
{}y^{\prime } y-\frac {a \left (\left (2+n \right ) x -2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {3 n +2}{n}}}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.940 |
|
|
\[
{}y^{\prime } y-\frac {a \left (\frac {\left (n +4\right ) x}{2+n}-2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (2+n \right )\right ) x^{-\frac {3 n +2}{n}}}{n \left (2+n \right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.061 |
|
|
\[
{}y^{\prime } y+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{3+n}} y}{3+n} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{3+n}}}{6+2 n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
11.928 |
|
|
\[
{}y^{\prime } y-a \left (\frac {2+n}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.958 |
|
|
\[
{}y^{\prime } y = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.614 |
|
|
\[
{}y^{\prime } y = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{\mu x} y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 \mu x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.444 |
|
|
\[
{}y^{\prime } y = \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.316 |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
87.284 |
|
|
\[
{}y^{\prime } y = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.443 |
|
|
\[
{}y^{\prime } y+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.456 |
|
|
\[
{}y^{\prime } y-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.500 |
|
|
\[
{}y^{\prime } y+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.959 |
|
|
\[
{}y^{\prime } y = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.446 |
|
|
\[
{}y^{\prime } y = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.546 |
|
|
\[
{}y^{\prime } y = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.888 |
|
|
\[
{}y^{\prime } y = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.315 |
|
|
\[
{}y^{\prime } y = a x \cos \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.905 |
|
|
\[
{}y^{\prime } y = a x \sin \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.944 |
|
|
\[
{}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.149 |
|
|
\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.625 |
|
|
\[
{}\left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -y^{2} a +2 a k x y+m y+k \left (k +b -m \right ) x +s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.650 |
|
|
\[
{}\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
35.935 |
|
|
\[
{}\left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.063 |
|
|
\[
{}x y y^{\prime } = y^{2} a +b y+c \,x^{n}+s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.234 |
|
|
\[
{}x y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.007 |
|
|
\[
{}y^{\prime \prime }+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.673 |
|
|
\[
{}y^{\prime \prime }-\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.931 |
|
|
\[
{}y^{\prime \prime }-\left (a^{2} x^{2}+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.958 |
|
|
\[
{}y^{\prime \prime }-\left (a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.519 |
|
|
\[
{}y^{\prime \prime }+a^{3} x \left (-a x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime \prime }-\left (a \,x^{2}+b c x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.563 |
|
|
\[
{}y^{\prime \prime }-a \,x^{n} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.867 |
|
|
\[
{}y^{\prime \prime }-a \left (a \,x^{2 n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.284 |
|
|
\[
{}y^{\prime \prime }-a \,x^{n -2} \left (a \,x^{n}+n +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.297 |
|
|
\[
{}y^{\prime \prime }+\left (a \,x^{2 n}+b \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.288 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.103 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.755 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }-\left (b \,x^{2}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.639 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2}+a x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.408 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b x \left (-b \,x^{3}+a x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.355 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}+a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
0.555 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \left (-b \,x^{2 n}-a \,x^{n}+n \,x^{n -1}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.553 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+\left (n -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.560 |
|
|
\[
{}y^{\prime \prime }-2 x y^{\prime }+2 n y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.538 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.614 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.597 |
|
|
\[
{}y^{\prime \prime }+a x y^{\prime }+\left (b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.661 |
|
|
\[
{}y^{\prime \prime }+2 a x y^{\prime }+\left (b \,x^{4}+a^{2} x^{2}+c x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.684 |
|
|
\[
{}y^{\prime \prime }+\left (a x +b \right ) y^{\prime }-a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.578 |
|