|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y y^{\prime }-y = 20 x +\frac {A}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.379 |
|
|
\[
{}y y^{\prime }-y = \frac {15 x}{4}+\frac {A}{x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.003 |
|
|
\[
{}y y^{\prime }-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.756 |
|
|
\[
{}y y^{\prime }-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.787 |
|
|
\[
{}y y^{\prime }-y = -\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.987 |
|
|
\[
{}y y^{\prime }-y = \frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.626 |
|
|
\[
{}y y^{\prime }-y = -\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
18.082 |
|
|
\[
{}y y^{\prime }-y = -\frac {5 x}{36}+\frac {A}{x^{{3}/{5}}}-\frac {B}{x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
11.755 |
|
|
\[
{}y y^{\prime }-y = \frac {k}{\sqrt {A \,x^{2}+B x +c}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.193 |
|
|
\[
{}y y^{\prime }-y = -\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.233 |
|
|
\[
{}y y^{\prime }-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
9.585 |
|
|
\[
{}y y^{\prime }-y = \frac {3 x}{4}-\frac {3 A \,x^{{1}/{3}}}{2}+\frac {3 A^{2}}{4 x^{{1}/{3}}}-\frac {27 A^{4}}{625 x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
9.507 |
|
|
\[
{}y y^{\prime }-y = -\frac {6 x}{25}+\frac {7 A \,x^{{1}/{3}}}{5}+\frac {31 A^{2}}{3 x^{{1}/{3}}}-\frac {100 A^{4}}{3 x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
9.432 |
|
|
\[
{}y y^{\prime }-y = -\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{{1}/{5}}}-\frac {7 A^{3}}{20 x^{{4}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
38.319 |
|
|
\[
{}y y^{\prime }-y = -\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{{5}/{11}}}-\frac {770 A^{3}}{9 x^{{13}/{11}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
37.775 |
|
|
\[
{}y y^{\prime }-y = -\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{{1}/{7}}}+\frac {280 A}{x^{{5}/{7}}}-\frac {400 A^{2}}{x^{{9}/{7}}}\right )}{9}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
41.313 |
|
|
\[
{}y y^{\prime }-y = a x +b \,x^{m}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.816 |
|
|
\[
{}y y^{\prime }-y = -\frac {\left (m +1\right ) x}{\left (m +2\right )^{2}}+A \,x^{2 m +1}+B \,x^{3 m +1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
12.563 |
|
|
\[
{}y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.708 |
|
|
\[
{}y y^{\prime }-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}+a \lambda x \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\lambda x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.844 |
|
|
\[
{}y y^{\prime }-y = 2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 a \sin \left (\lambda x \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.098 |
|
|
\[
{}y y^{\prime }-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
101.948 |
|
|
\[
{}y y^{\prime } = \left (a x +b \right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.075 |
|
|
\[
{}y y^{\prime } = \frac {y}{\left (a x +b \right )^{2}}+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.124 |
|
|
\[
{}y y^{\prime } = \left (a -\frac {1}{a x}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.979 |
|
|
\[
{}y y^{\prime } = \frac {y}{\sqrt {a x +b}}+1
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
13.960 |
|
|
\[
{}y y^{\prime } = \frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.014 |
|
|
\[
{}y y^{\prime } = \left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.619 |
|
|
\[
{}y y^{\prime } = a \,{\mathrm e}^{\lambda x} y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.358 |
|
|
\[
{}y y^{\prime } = \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.084 |
|
|
\[
{}y y^{\prime } = a y \cosh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.329 |
|
|
\[
{}y y^{\prime } = a y \sinh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.459 |
|
|
\[
{}y y^{\prime } = a \cos \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.748 |
|
|
\[
{}y y^{\prime } = a \sin \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.907 |
|
|
\[
{}y y^{\prime } = \left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.097 |
|
|
\[
{}y y^{\prime } = \left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.385 |
|
|
\[
{}2 y y^{\prime } = \left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.263 |
|
|
\[
{}y y^{\prime } = \left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.356 |
|
|
\[
{}y y^{\prime }+x \left (a \,x^{2}+b \right ) y+x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.142 |
|
|
\[
{}y y^{\prime }+a \left (1-\frac {1}{x}\right ) y = a^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.970 |
|
|
\[
{}y y^{\prime }-a \left (1-\frac {b}{x}\right ) y = a^{2} b
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.006 |
|
|
\[
{}y y^{\prime } = x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.505 |
|
|
\[
{}y y^{\prime } = a \left (-n b +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.953 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y+\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
44.030 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
64.950 |
|
|
\[
{}y y^{\prime } = \frac {\left (\left (m +2 L -3\right ) x +n -2 L +3\right ) y}{x}+\left (\left (m -L -1\right ) x^{2}+\left (n -m -2 L +3\right ) x -n +L -2\right ) x^{1-2 L}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
18.049 |
|
|
\[
{}y y^{\prime } = \left (a \left (2 n +1\right ) x^{2}+c x +b \left (2 n -1\right )\right ) x^{n -2} y-\left (n \,a^{2} x^{4}+a c \,x^{3}+n \,b^{2}+b c x +d \,x^{2}\right ) x^{2 n -3}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
12.145 |
|
|
\[
{}y y^{\prime } = \left (a \left (n -1\right ) x +b \left (2 \lambda +n \right )\right ) x^{\lambda -1} \left (a x +b \right )^{-\lambda -2} y-\left (a n x +b \left (\lambda +n \right )\right ) x^{2 \lambda -1} \left (a x +b \right )^{-2 \lambda -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
62.452 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (m -1\right ) x +1\right ) y}{x} = \frac {a^{2} \left (m x +1\right ) \left (-1+x \right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.111 |
|
|
\[
{}y y^{\prime }-a \left (1-\frac {b}{\sqrt {x}}\right ) y = \frac {a^{2} b}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.046 |
|
|
\[
{}y y^{\prime } = \frac {3 y}{\left (a x +b \right )^{{1}/{3}} x^{{5}/{3}}}+\frac {3}{\left (a x +b \right )^{{2}/{3}} x^{{7}/{3}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.474 |
|
|
\[
{}3 y y^{\prime } = \frac {\left (-7 \lambda s \left (3 s +4 \lambda \right ) x +6 s -2 \lambda \right ) y}{x^{{1}/{3}}}+\frac {6 \lambda s x -6}{x^{{2}/{3}}}+2 \left (\lambda s \left (3 s +4 \lambda \right ) x +5 \lambda \right ) \left (-\lambda s \left (3 s +4 \lambda \right ) x +3 s +4 \lambda \right ) x^{{1}/{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
23.381 |
|
|
\[
{}y y^{\prime }+\frac {a \left (6 x -1\right ) y}{2 x} = -\frac {a^{2} \left (-1+x \right ) \left (4 x -1\right )}{2 x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.606 |
|
|
\[
{}y y^{\prime }-\frac {a \left (1+\frac {2 b}{x^{2}}\right ) y}{2} = \frac {a^{2} \left (3 x +\frac {4 b}{x}\right )}{16}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.680 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -20\right ) y}{14 x^{{9}/{7}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (x -8\right )}{14 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
85.418 |
|
|
\[
{}y y^{\prime }+\frac {5 a \left (23 x -16\right ) y}{56 x^{{9}/{7}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (25 x -32\right )}{56 x^{{11}/{17}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
89.308 |
|
|
\[
{}y y^{\prime }+\frac {a \left (19 x +85\right ) y}{26 x^{{18}/{13}}} = -\frac {3 a^{2} \left (-1+x \right ) \left (x +25\right )}{26 x^{{23}/{13}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
20.792 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -18\right ) y}{15 x^{{7}/{5}}} = -\frac {4 a^{2} \left (-1+x \right ) \left (x -6\right )}{15 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.451 |
|
|
\[
{}y y^{\prime }+\frac {a \left (1+5 x \right ) y}{2 \sqrt {x}} = a^{2} \left (-x^{2}+1\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.997 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (19 x -14\right ) x^{{7}/{5}} y}{35} = -\frac {4 a^{2} \left (-1+x \right ) \left (9 x -14\right ) x^{{9}/{5}}}{35}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.218 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (3 x +7\right ) y}{10 x^{{13}/{10}}} = -\frac {a^{2} \left (-1+x \right ) \left (x +9\right )}{5 x^{{8}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
88.118 |
|
|
\[
{}y y^{\prime }+\frac {a \left (7 x -12\right ) y}{10 x^{{7}/{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -16\right )}{10 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.898 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (13 x -8\right ) y}{20 x^{{7}/{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (27 x -32\right )}{20 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.890 |
|
|
\[
{}y y^{\prime }+\frac {3 a \left (3 x +11\right ) y}{14 x^{{10}/{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -27\right )}{14 x^{{13}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.444 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
29.418 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +1\right ) y}{2 x^{{7}/{4}}} = \frac {a^{2} \left (-1+x \right ) \left (x +5\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
29.464 |
|
|
\[
{}y y^{\prime }-\frac {a \left (4 x +3\right ) y}{14 x^{{8}/{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (16 x +5\right )}{14 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.930 |
|
|
\[
{}y y^{\prime }+\frac {a \left (13 x -3\right ) y}{6 x^{{2}/{3}}} = -\frac {a^{2} \left (-1+x \right ) \left (5 x -1\right )}{6 x^{{1}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
12.533 |
|
|
\[
{}y y^{\prime }-\frac {a \left (8 x -1\right ) y}{28 x^{{8}/{7}}} = \frac {a^{2} \left (-1+x \right ) \left (32 x +3\right )}{28 x^{{9}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.773 |
|
|
\[
{}y y^{\prime }-\frac {a \left (5 x -4\right ) y}{x^{4}} = \frac {a^{2} \left (-1+x \right ) \left (3 x -1\right )}{x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.782 |
|
|
\[
{}y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}} = \frac {a^{2} \left (-1+x \right ) \left (8 x -5\right )}{5 x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.924 |
|
|
\[
{}y y^{\prime }+\frac {a \left (39 x -4\right ) y}{42 x^{{9}/{7}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -1\right )}{42 x^{{11}/{7}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.534 |
|
|
\[
{}y y^{\prime }+\frac {a \left (-2+x \right ) y}{x} = \frac {2 a^{2} \left (-1+x \right )}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.243 |
|
|
\[
{}y y^{\prime }+\frac {a \left (3 x -2\right ) y}{x} = -\frac {2 a^{2} \left (-1+x \right )^{2}}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.758 |
|
|
\[
{}y y^{\prime }+\frac {a \left (1-\frac {b}{x^{2}}\right ) y}{x} = \frac {a^{2} b}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.495 |
|
|
\[
{}y y^{\prime }-\frac {a \left (-4+3 x \right ) y}{4 x^{{5}/{2}}} = \frac {a^{2} \left (-1+x \right ) \left (x +2\right )}{4 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.682 |
|
|
\[
{}y y^{\prime }+\frac {a \left (33 x +2\right ) y}{30 x^{{6}/{5}}} = -\frac {a^{2} \left (-1+x \right ) \left (9 x -4\right )}{30 x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.211 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x -8\right ) y}{8 x^{{5}/{2}}} = -\frac {a^{2} \left (-1+x \right ) \left (-4+3 x \right )}{8 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.191 |
|
|
\[
{}y y^{\prime }+\frac {a \left (17 x +18\right ) y}{30 x^{{22}/{15}}} = -\frac {a^{2} \left (-1+x \right ) \left (x +4\right )}{30 x^{{29}/{15}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
87.181 |
|
|
\[
{}y y^{\prime }-\frac {a \left (6 x -13\right ) y}{13 x^{{5}/{2}}} = -\frac {a^{2} \left (-1+x \right ) \left (x -13\right )}{26 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.210 |
|
|
\[
{}y y^{\prime }+\frac {a \left (24 x +11\right ) x^{{27}/{20}} y}{30} = -\frac {a^{2} \left (-1+x \right ) \left (9 x +1\right )}{60 x^{{17}/{10}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
105.130 |
|
|
\[
{}y y^{\prime }-\frac {2 a \left (3 x +2\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (-1+x \right ) \left (8 x +1\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.980 |
|
|
\[
{}y y^{\prime }-\frac {6 a \left (4 x +1\right ) y}{5 x^{{7}/{5}}} = \frac {a^{2} \left (-1+x \right ) \left (27 x +8\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.820 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{3}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.694 |
|
|
\[
{}y y^{\prime }-\frac {a \left (x +4\right ) y}{5 x^{{8}/{5}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +7\right )}{5 x^{{11}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.809 |
|
|
\[
{}y y^{\prime }-\frac {a \left (2 x -1\right ) y}{x^{{5}/{2}}} = \frac {a^{2} \left (-1+x \right ) \left (3 x +1\right )}{2 x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.716 |
|
|
\[
{}y y^{\prime }+\frac {a \left (x -6\right ) y}{5 x^{{7}/{5}}} = \frac {2 a^{2} \left (-1+x \right ) \left (x +4\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.352 |
|
|
\[
{}y y^{\prime }+\frac {a \left (21 x +19\right ) y}{5 x^{{7}/{5}}} = -\frac {2 a^{2} \left (-1+x \right ) \left (9 x -4\right )}{5 x^{{9}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
17.127 |
|
|
\[
{}y y^{\prime }-\frac {3 a y}{x^{{7}/{4}}} = \frac {a^{2} \left (-1+x \right ) \left (x -9\right )}{4 x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
24.287 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (k +1\right ) x -1\right ) y}{x^{2}} = \frac {a^{2} \left (k +1\right ) \left (-1+x \right )}{x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.082 |
|
|
\[
{}y y^{\prime }-a \left (\left (k -2\right ) x +2 k -3\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (-1+x \right )^{2} x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.585 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (4 k -7\right ) x -4 k +5\right ) x^{-k} y}{2} = \frac {a^{2} \left (2 k -3\right ) \left (-1+x \right )^{2} x^{1-2 k}}{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.245 |
|
|
\[
{}y y^{\prime }-\left (\left (2 n -1\right ) x -a n \right ) x^{-1-n} y = n \left (x -a \right ) x^{-2 n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.181 |
|
|
\[
{}y y^{\prime }-\left (\left (n +1\right ) x -a n \right ) x^{n -1} \left (x -a \right )^{-n -2} y = n \,x^{2 n} \left (x -a \right )^{-2 n -3}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
13.445 |
|
|
\[
{}y y^{\prime }-a \left (\left (2 k -3\right ) x +1\right ) x^{-k} y = a^{2} \left (k -2\right ) \left (\left (k -1\right ) x +1\right ) x^{2-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
6.550 |
|
|
\[
{}y y^{\prime }-a \left (\left (n +2 k -3\right ) x +3-2 k \right ) x^{-k} y = a^{2} \left (\left (n +k -1\right ) x^{2}-\left (n +2 k -3\right ) x +k -2\right ) x^{1-2 k}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
10.011 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\left (2+n \right ) x -2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (\left (n +1\right ) x^{2}-2 x -n +1\right ) x^{-\frac {3 n +2}{n}}}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.339 |
|
|
\[
{}y y^{\prime }-\frac {a \left (\frac {\left (n +4\right ) x}{2+n}-2\right ) x^{-\frac {2 n +1}{n}} y}{n} = \frac {a^{2} \left (2 x^{2}+\left (n^{2}+n -4\right ) x -\left (n -1\right ) \left (2+n \right )\right ) x^{-\frac {3 n +2}{n}}}{n \left (2+n \right )}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
8.875 |
|
|
\[
{}y y^{\prime }+\frac {a \left (\frac {\left (3 n +5\right ) x}{2}+\frac {n -1}{n +1}\right ) x^{-\frac {n +4}{3+n}} y}{3+n} = -\frac {a^{2} \left (\left (n +1\right ) x^{2}-\frac {\left (n^{2}+2 n +5\right ) x}{n +1}+\frac {4}{n +1}\right ) x^{-\frac {n +5}{3+n}}}{6+2 n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
13.161 |
|
|
\[
{}y y^{\prime }-a \left (\frac {2+n}{n}+b \,x^{n}\right ) y = -\frac {a^{2} x \left (\frac {n +1}{n}+b \,x^{n}\right )}{n}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
3.553 |
|