|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.365 |
|
|
\[
{}y y^{\prime } = \left (a x +b \right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.937 |
|
|
\[
{}y y^{\prime } = \frac {y}{\left (a x +b \right )^{2}}+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.631 |
|
|
\[
{}y y^{\prime } = \left (a -\frac {1}{a x}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.909 |
|
|
\[
{}y y^{\prime } = \frac {y}{\sqrt {a x +b}}+1
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.444 |
|
|
\[
{}y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.286 |
|
|
\[
{}y y^{\prime } = \left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.750 |
|
|
\[
{}y y^{\prime } = a \,{\mathrm e}^{\lambda x} y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.125 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.657 |
|
|
\[
{}y y^{\prime } = a y \cosh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.789 |
|
|
\[
{}y y^{\prime } = a y \sinh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.980 |
|
|
\[
{}y y^{\prime } = a \cos \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.046 |
|
|
\[
{}y y^{\prime } = a \sin \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.220 |
|
|
\[
{}y y^{\prime } = \left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.732 |
|
|
\[
{}y y^{\prime } = \left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.042 |
|
|
\[
{}2 y y^{\prime } = \left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.515 |
|
|
\[
{}y y^{\prime } = \left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.152 |
|
|
\[
{}y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.145 |
|
|
\[
{}y y^{\prime }+a \left (1-\frac {1}{x}\right ) y = a^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.871 |
|
|
\[
{}y y^{\prime }-a \left (1-\frac {b}{x}\right ) y = a^{2} b
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.927 |
|
|
\[
{}y y^{\prime } = x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.866 |
|
|
\[
{}y y^{\prime } = a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.537 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y+\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
41.776 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
62.603 |
|
|
\[
{}y y^{\prime } = \frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}+\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
14.283 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +1\right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.967 |
|
|
\[
{}y y^{\prime } = \left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
28.644 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (x -1\right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.196 |
|
|
\[
{}y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y = \frac {a^{2} b}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.343 |
|
|
\[
{}y y^{\prime } = \frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.000 |
|
|
\[
{}3 y y^{\prime } = \frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{{1}/{3}}}+\frac {6 \lambda s x -6}{x^{{2}/{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{{1}/{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
21.140 |
|
|
\[
{}y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (x -1\right ) \left (4 x -1\right )}{2 x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.210 |
|
|
\[
{}y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2} = \frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.599 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x -8\right )}{14 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
80.126 |
|
|
\[
{}y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{{9}/{7}}} = -\frac {3 a^{2} \left (x -1\right ) \left (25 x -32\right )}{56 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
99.704 |
|
|
\[
{}y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}} = -\frac {3 a^{2} \left (x -1\right ) \left (x +25\right )}{26 x^{{23}/{13}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
23.154 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}} = -\frac {4 a^{2} \left (x -1\right ) \left (x -6\right )}{15 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.113 |
|
|
\[
{}y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}} = a^{2} \left (-x^{2}+1\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.481 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35} = -\frac {4 a^{2} \left (x -1\right ) \left (9 x -14\right ) x^{{9}/{5}}}{35}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.418 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (3 x +7\right ) y}{10 x^{{13}/{10}}} = -\frac {a^{2} \left (x -1\right ) \left (x +9\right )}{5 x^{{8}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
79.074 |
|
|
\[
{}y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (x -16\right )}{10 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.435 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (27 x -32\right )}{20 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.514 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (x -27\right )}{14 x^{{13}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.671 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
24.288 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
24.585 |
|
|
\[
{}y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (16 x +5\right )}{14 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.068 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}} = -\frac {a^{2} \left (x -1\right ) \left (5 x -1\right )}{6 x^{{1}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
12.364 |
|
|
\[
{}y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{{8}/{7}}} = \frac {a^{2} \left (x -1\right ) \left (32 x +3\right )}{28 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.253 |
|
|
\[
{}y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (x -1\right ) \left (3 x -1\right )}{x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.638 |
|
|
\[
{}y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}} = \frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.674 |
|
|
\[
{}y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -1\right )}{42 x^{{11}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.093 |
|
|
\[
{}y y^{\prime }+\frac {a \left (x -2\right ) y}{x} = \frac {2 a^{2} \left (x -1\right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.130 |
|
|
\[
{}y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x} = -\frac {2 a^{2} \left (x -1\right )^{2}}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.681 |
|
|
\[
{}y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x} = \frac {a^{2} b}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.454 |
|
|
\[
{}y y^{\prime }-\frac {a \left (3 x -4\right ) y}{4 x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (x +2\right )}{4 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.138 |
|
|
\[
{}y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}} = -\frac {a^{2} \left (x -1\right ) \left (9 x -4\right )}{30 x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.279 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}} = -\frac {a^{2} \left (x -1\right ) \left (3 x -4\right )}{8 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.285 |
|
|
\[
{}y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{{22}/{15}}} = -\frac {a^{2} \left (x -1\right ) \left (x +4\right )}{30 x^{{29}/{15}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
77.245 |
|
|
\[
{}y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}} = -\frac {a^{2} \left (x -1\right ) \left (x -13\right )}{26 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.008 |
|
|
\[
{}y y^{\prime }+\frac {a \left (24 x +11\right ) x^{{27}/{20}} y}{30} = -\frac {a^{2} \left (x -1\right ) \left (9 x +1\right )}{60 x^{{17}/{10}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
96.272 |
|
|
\[
{}y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (8 x +1\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.355 |
|
|
\[
{}y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (27 x +8\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.889 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{3}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.255 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +7\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.202 |
|
|
\[
{}y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}} = \frac {a^{2} \left (x -1\right ) \left (3 x +1\right )}{2 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.421 |
|
|
\[
{}y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}} = \frac {2 a^{2} \left (x -1\right ) \left (x +4\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.003 |
|
|
\[
{}y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{{7}/{5}}} = -\frac {2 a^{2} \left (x -1\right ) \left (9 x -4\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
16.983 |
|
|
\[
{}y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}} = \frac {a^{2} \left (x -1\right ) \left (x -9\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
12.550 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (k +1\right ) \left (x -1\right )}{x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.581 |
|
|
\[
{}y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (x -1\right )^{2} x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.261 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2} = \frac {a^{2} \left (2 k -3\right ) \left (x -1\right )^{2} x^{1-2 k}}{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.586 |
|
|
\[
{}y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-n -1} y = n \left (x -a \right ) x^{-2 n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.954 |
|
|
\[
{}y y^{\prime }-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y = n \,x^{2 n} \left (x -a \right )^{-2 n -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
10.679 |
|
|
\[
{}y y^{\prime }-a \left (\left (2 k -3\right ) x +1\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{2-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.192 |
|
|
\[
{}y y^{\prime }-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y = a^{2} \left (\left (n +k -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.417 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (n +2\right ) x -2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {3 n +2}{n}}}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.424 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{n +2}-2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (n +2\right )\right ) x^{-\frac {3 n +2}{n}}}{n \left (n +2\right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.691 |
|
|
\[
{}y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{n +3}} y}{n +3} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{n +3}}}{2 n +6}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
11.279 |
|
|
\[
{}y y^{\prime }-a \left (\frac {n +2}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.925 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{x}+b \right ) y+c \,{\mathrm e}^{2 x}-a b \,{\mathrm e}^{x}-b^{2}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.595 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 \mu +\lambda \right ) {\mathrm e}^{\lambda x}+b \right ) {\mathrm e}^{\mu x} y+\left (-a^{2} \mu \,{\mathrm e}^{2 \lambda x}-a b \,{\mathrm e}^{\lambda x}+c \right ) {\mathrm e}^{2 \mu x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.085 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{\lambda x}+b \right ) y+c \left (a^{2} {\mathrm e}^{2 \lambda x}+a b \left (\lambda x +1\right ) {\mathrm e}^{\lambda x}+b^{2} \lambda x \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.314 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{\lambda x} \left (2 a \lambda x +a +b \right ) y-{\mathrm e}^{2 \lambda x} \left (a^{2} \lambda \,x^{2}+a b x +c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
88.332 |
|
|
\[
{}y y^{\prime } = {\mathrm e}^{a x} \left (2 a \,x^{2}+b +2 x \right ) y+{\mathrm e}^{2 a x} \left (-a \,x^{4}-b \,x^{2}+c \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.431 |
|
|
\[
{}y y^{\prime }+a \left (2 b x +1\right ) {\mathrm e}^{b x} y = -a^{2} b \,x^{2} {\mathrm e}^{2 b x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.498 |
|
|
\[
{}y y^{\prime }-a \left (1+2 n +2 n \left (n +1\right ) x \right ) {\mathrm e}^{\left (n +1\right ) x} y = -a^{2} n \left (n +1\right ) \left (n x +1\right ) x \,{\mathrm e}^{2 \left (n +1\right ) x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.512 |
|
|
\[
{}y y^{\prime }+a \left (1+2 b \sqrt {x}\right ) {\mathrm e}^{2 b \sqrt {x}} y = -a^{2} b \,x^{{3}/{2}} {\mathrm e}^{4 b \sqrt {x}}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.036 |
|
|
\[
{}y y^{\prime } = \left (a \cosh \left (x \right )+b \right ) y-a b \sinh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.133 |
|
|
\[
{}y y^{\prime } = \left (a \sinh \left (x \right )+b \right ) y-a b \cosh \left (x \right )+c
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.564 |
|
|
\[
{}y y^{\prime } = \left (2 \ln \left (x \right )+a +1\right ) y+x \left (-\ln \left (x \right )^{2}-a \ln \left (x \right )+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.863 |
|
|
\[
{}y y^{\prime } = \left (2 \ln \left (x \right )^{2}+2 \ln \left (x \right )+a \right ) y+x \left (-\ln \left (x \right )^{4}-a \ln \left (x \right )^{2}+b \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.140 |
|
|
\[
{}y y^{\prime } = a x \cos \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.608 |
|
|
\[
{}y y^{\prime } = a x \sin \left (\lambda \,x^{2}\right ) y+x
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.879 |
|
|
\[
{}\left (A y+B x +a \right ) y^{\prime }+B y+k x +b = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.666 |
|
|
\[
{}\left (y+a x +b \right ) y^{\prime } = \alpha y+\beta x +\gamma
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.302 |
|
|
\[
{}\left (y+a k \,x^{2}+b x +c \right ) y^{\prime } = -a y^{2}+2 a k x y+m y+k \left (k +b -m \right ) x +s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.173 |
|
|
\[
{}\left (y+A \,x^{n}+a \right ) y^{\prime }+n A \,x^{n -1} y+k \,x^{m}+b = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
35.770 |
|
|
\[
{}\left (y+a \,x^{n +1}+b \,x^{n}\right ) y^{\prime } = \left (a n \,x^{n}+c \,x^{n -1}\right ) y
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.834 |
|
|
\[
{}x y y^{\prime } = a y^{2}+b y+c \,x^{n}+s
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.135 |
|
|
\[
{}x y y^{\prime } = -n y^{2}+a \left (2 n +1\right ) x y+b y-a^{2} n \,x^{2}-a b x +c
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.954 |
|