|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = y^{2}+\lambda ^{2}+\frac {f \left (\frac {\sin \left (\lambda x +a \right )}{\sin \left (\lambda x +b \right )}\right )}{\sin \left (\lambda x +b \right )^{4}}
\] |
[_Riccati] |
✗ |
455.068 |
|
|
\[
{}y^{\prime } y-y = A
\] |
[_quadrature] |
✓ |
1.241 |
|
|
\[
{}y^{\prime } y-y = A x +B
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.441 |
|
|
\[
{}y^{\prime } y-y = -\frac {2 x}{9}+A +\frac {B}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.180 |
|
|
\[
{}y^{\prime } y-y = 2 A \left (\sqrt {x}+4 A +\frac {3 A^{2}}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.806 |
|
|
\[
{}y^{\prime } y-y = A x +\frac {B}{x}-\frac {B^{2}}{x^{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.407 |
|
|
\[
{}y^{\prime } y-y = A \,x^{k -1}-k B \,x^{k}+k \,B^{2} x^{2 k -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.553 |
|
|
\[
{}y^{\prime } y-y = \frac {A}{x}-\frac {A^{2}}{x^{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.270 |
|
|
\[
{}y^{\prime } y-y = A +B \,{\mathrm e}^{-\frac {2 x}{A}}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.391 |
|
|
\[
{}y^{\prime } y-y = A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.353 |
|
|
\[
{}y^{\prime } y-y = -\frac {2 \left (m +1\right )}{\left (3+m \right )^{2}}+A \,x^{m}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.132 |
|
|
\[
{}y^{\prime } y-y = -\frac {2 x}{9}+6 A^{2} \left (1+\frac {2 A}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.291 |
|
|
\[
{}y^{\prime } y-y = \frac {2 m -2}{\left (m -3\right )^{2}}+\frac {2 A \left (m \left (3+m \right ) \sqrt {x}+\left (4 m^{2}+3 m +9\right ) A +\frac {3 m \left (3+m \right ) A^{2}}{\sqrt {x}}\right )}{\left (m -3\right )^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
40.360 |
|
|
\[
{}y^{\prime } y-y = \frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.899 |
|
|
\[
{}y^{\prime } y-y = \frac {4}{9} x +2 A \,x^{2}+2 A^{2} x^{3}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.370 |
|
|
\[
{}y^{\prime } y-y = -\frac {3 x}{16}+\frac {5 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.474 |
|
|
\[
{}y^{\prime } y-y = \frac {A}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.656 |
|
|
\[
{}y^{\prime } y-y = -\frac {x}{4}+\frac {A \left (\sqrt {x}+5 A +\frac {3 A^{2}}{\sqrt {x}}\right )}{4}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.684 |
|
|
\[
{}y^{\prime } y-y = \frac {2 a^{2}}{\sqrt {8 a^{2}+x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.276 |
|
|
\[
{}y^{\prime } y-y = 2 x +\frac {A}{x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.996 |
|
|
\[
{}y^{\prime } y-y = -\frac {6 X}{25}+\frac {2 A \left (2 \sqrt {x}+19 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{25}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
26.868 |
|
|
\[
{}y^{\prime } y-y = \frac {3 x}{8}+\frac {3 \sqrt {a^{2}+x^{2}}}{8}-\frac {a^{2}}{16 \sqrt {a^{2}+x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.482 |
|
|
\[
{}y^{\prime } y-y = -\frac {4 x}{25}+\frac {A}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.967 |
|
|
\[
{}y^{\prime } y-y = -\frac {9 x}{100}+\frac {A}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
40.179 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {2 A \left (5 \sqrt {x}+34 A +\frac {15 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.218 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {A \left (25 \sqrt {x}+41 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{98}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.052 |
|
|
\[
{}y^{\prime } y-y = -\frac {2 x}{9}+\frac {A}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.683 |
|
|
\[
{}y^{\prime } y-y = -\frac {5 x}{36}+\frac {A}{x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
47.165 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {6 A \left (-3 \sqrt {x}+23 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.835 |
|
|
\[
{}y^{\prime } y-y = -\frac {30 x}{121}+\frac {3 A \left (21 \sqrt {x}+35 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{242}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.452 |
|
|
\[
{}y^{\prime } y-y = -\frac {3 x}{16}+\frac {A}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
39.495 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {4 A \left (-10 \sqrt {x}+27 A +\frac {10 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.447 |
|
|
\[
{}y^{\prime } y-y = \frac {A}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.728 |
|
|
\[
{}y^{\prime } y-y = \frac {A}{x^{2}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.686 |
|
|
\[
{}y^{\prime } y-y = A \left (2+n \right ) \left (\sqrt {x}+2 \left (2+n \right ) A +\frac {\left (n +1\right ) \left (3+n \right ) A^{2}}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
18.512 |
|
|
\[
{}y^{\prime } y-y = A \left (2+n \right ) \left (\sqrt {x}+2 \left (2+n \right ) A +\frac {\left (2 n +3\right ) A^{2}}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
18.201 |
|
|
\[
{}y^{\prime } y-y = A \sqrt {x}+2 A^{2}+\frac {B}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
11.721 |
|
|
\[
{}y^{\prime } y-y = 2 A^{2}-A \sqrt {x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.027 |
|
|
\[
{}y^{\prime } y-y = -\frac {x}{4}+\frac {6 A \left (\sqrt {x}+8 A +\frac {5 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.283 |
|
|
\[
{}y^{\prime } y-y = -\frac {6 x}{25}+\frac {6 A \left (2 \sqrt {x}+7 A +\frac {4 A^{2}}{\sqrt {x}}\right )}{25}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.774 |
|
|
\[
{}y^{\prime } y-y = -\frac {3 x}{16}+\frac {3 A}{x^{{1}/{3}}}-\frac {12 A^{2}}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.810 |
|
|
\[
{}y^{\prime } y-y = \frac {3 x}{8}+\frac {3 \sqrt {b^{2}+x^{2}}}{8}+\frac {3 b^{2}}{16 \sqrt {b^{2}+x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.223 |
|
|
\[
{}y^{\prime } y-y = \frac {9 x}{32}+\frac {15 \sqrt {b^{2}+x^{2}}}{32}+\frac {3 b^{2}}{64 \sqrt {b^{2}+x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.583 |
|
|
\[
{}y^{\prime } y-y = -\frac {3 x}{32}-\frac {3 \sqrt {a^{2}+x^{2}}}{32}+\frac {15 a^{2}}{64 \sqrt {a^{2}+x^{2}}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.657 |
|
|
\[
{}y^{\prime } y-y = A \,x^{2}-\frac {9}{625 A}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.061 |
|
|
\[
{}y^{\prime } y-y = -\frac {6}{25} x -A \,x^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.919 |
|
|
\[
{}y^{\prime } y-y = \frac {6}{25} x -A \,x^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.901 |
|
|
\[
{}y^{\prime } y-y = 12 x +\frac {A}{x^{{5}/{2}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.463 |
|
|
\[
{}y^{\prime } y-y = \frac {63 x}{4}+\frac {A}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
45.556 |
|
|
\[
{}y^{\prime } y-y = 2 x +2 A \left (10 \sqrt {x}+31 A +\frac {30 A^{2}}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.883 |
|
|
\[
{}y^{\prime } y-y = 2 x +2 A \left (-10 \sqrt {x}+19 A +\frac {30 A^{2}}{\sqrt {x}}\right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.666 |
|
|
\[
{}y^{\prime } y-y = -\frac {28 x}{121}+\frac {2 A \left (5 \sqrt {x}+106 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{121}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.944 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {A \left (5 \sqrt {x}+262 A +\frac {65 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.064 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+A \sqrt {x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
4.053 |
|
|
\[
{}y^{\prime } y-y = 6 x +\frac {A}{x^{4}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.905 |
|
|
\[
{}y^{\prime } y-y = 20 x +\frac {A}{\sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.848 |
|
|
\[
{}y^{\prime } y-y = \frac {15 x}{4}+\frac {A}{x^{7}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.980 |
|
|
\[
{}y^{\prime } y-y = -\frac {10 x}{49}+\frac {2 A \left (4 \sqrt {x}+61 A +\frac {12 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.411 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+\frac {2 A \left (\sqrt {x}+166 A +\frac {55 A^{2}}{\sqrt {x}}\right )}{49}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.010 |
|
|
\[
{}y^{\prime } y-y = -\frac {4 x}{25}+\frac {A \left (7 \sqrt {x}+49 A +\frac {6 A^{2}}{\sqrt {x}}\right )}{50}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.950 |
|
|
\[
{}y^{\prime } y-y = \frac {15 x}{4}+\frac {6 A}{x^{{1}/{3}}}-\frac {3 A^{2}}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
4.733 |
|
|
\[
{}y^{\prime } y-y = -\frac {3 x}{16}+\frac {A}{x^{{1}/{3}}}+\frac {B}{x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
16.858 |
|
|
\[
{}y^{\prime } y-y = -\frac {5 x}{36}+\frac {A}{x^{{3}/{5}}}-\frac {B}{x^{{7}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
9.607 |
|
|
\[
{}y^{\prime } y-y = \frac {k}{\sqrt {A \,x^{2}+B x +c}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.995 |
|
|
\[
{}y^{\prime } y-y = -\frac {12 x}{49}+3 A \left (\frac {1}{49}+B \right ) \sqrt {x}+3 A^{2} \left (\frac {4}{49}-\frac {5 B}{2}\right )+\frac {15 A^{3} \left (\frac {1}{49}-\frac {5 B}{4}\right )}{4 \sqrt {x}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.351 |
|
|
\[
{}y^{\prime } y-y = -\frac {6 x}{25}+\frac {4 B^{2} \left (\left (2-A \right ) x^{{1}/{3}}-\frac {3 B \left (2 A +1\right )}{2}+\frac {B^{2} \left (1-3 A \right )}{x^{{1}/{3}}}-\frac {A \,B^{3}}{x^{{2}/{3}}}\right )}{75}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
6.791 |
|
|
\[
{}y^{\prime } y-y = \frac {3 x}{4}-\frac {3 A \,x^{{1}/{3}}}{2}+\frac {3 A^{2}}{4 x^{{1}/{3}}}-\frac {27 A^{4}}{625 x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.480 |
|
|
\[
{}y^{\prime } y-y = -\frac {6 x}{25}+\frac {7 A \,x^{{1}/{3}}}{5}+\frac {31 A^{2}}{3 x^{{1}/{3}}}-\frac {100 A^{4}}{3 x^{{5}/{3}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
8.276 |
|
|
\[
{}y^{\prime } y-y = -\frac {10 x}{49}+\frac {13 A^{2}}{5 x^{{1}/{5}}}-\frac {7 A^{3}}{20 x^{{4}/{5}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
15.621 |
|
|
\[
{}y^{\prime } y-y = -\frac {33 x}{169}+\frac {286 A^{2}}{3 x^{{5}/{11}}}-\frac {770 A^{3}}{9 x^{{13}/{11}}}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
37.077 |
|
|
\[
{}y^{\prime } y-y = -\frac {21 x}{100}+\frac {7 A^{2} \left (\frac {123}{x^{{1}/{7}}}+\frac {280 A}{x^{{5}/{7}}}-\frac {400 A^{2}}{x^{{9}/{7}}}\right )}{9}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
39.836 |
|
|
\[
{}y^{\prime } y-y = a x +b \,x^{m}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.583 |
|
|
\[
{}y^{\prime } y-y = -\frac {\left (m +1\right ) x}{\left (2+m \right )^{2}}+A \,x^{2 m +1}+B \,x^{3 m +1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
12.594 |
|
|
\[
{}y^{\prime } y-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}-a \left (b \lambda +1\right ) {\mathrm e}^{\lambda x}+b
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.660 |
|
|
\[
{}y^{\prime } y-y = a^{2} \lambda \,{\mathrm e}^{2 \lambda x}+a \lambda x \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\lambda x}
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.345 |
|
|
\[
{}y^{\prime } y-y = 2 a^{2} \lambda \sin \left (2 \lambda x \right )+2 a \sin \left (\lambda x \right )
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.234 |
|
|
\[
{}y^{\prime } y-y = a^{2} f^{\prime }\left (x \right ) f^{\prime \prime }\left (x \right )-\frac {\left (f \left (x \right )+b \right )^{2} f^{\prime \prime }\left (x \right )}{{f^{\prime }\left (x \right )}^{3}}
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.915 |
|
|
\[
{}y^{\prime } y = \left (a x +b \right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
0.953 |
|
|
\[
{}y^{\prime } y = \frac {y}{\left (a x +b \right )^{2}}+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.651 |
|
|
\[
{}y^{\prime } y = \left (a -\frac {1}{a x}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.919 |
|
|
\[
{}y^{\prime } y = \frac {y}{\sqrt {a x +b}}+1
\] |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
11.649 |
|
|
\[
{}y^{\prime } y = \frac {3 y}{\sqrt {a \,x^{{3}/{2}}+8 x}}+1
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
3.243 |
|
|
\[
{}y^{\prime } y = \left (\frac {a}{x^{{2}/{3}}}-\frac {2}{3 a \,x^{{1}/{3}}}\right ) y+1
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
2.715 |
|
|
\[
{}y^{\prime } y = a \,{\mathrm e}^{\lambda x} y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.138 |
|
|
\[
{}y^{\prime } y = \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{-\lambda x}\right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.716 |
|
|
\[
{}y^{\prime } y = a y \cosh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.924 |
|
|
\[
{}y^{\prime } y = a y \sinh \left (x \right )+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.040 |
|
|
\[
{}y^{\prime } y = a \cos \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.179 |
|
|
\[
{}y^{\prime } y = a \sin \left (\lambda x \right ) y+1
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.350 |
|
|
\[
{}y^{\prime } y = \left (a x +3 b \right ) y+c \,x^{3}-a b \,x^{2}-2 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.765 |
|
|
\[
{}y^{\prime } y = \left (3 a x +b \right ) y-a^{2} x^{3}-a b \,x^{2}+c x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.182 |
|
|
\[
{}2 y^{\prime } y = \left (7 a x +5 b \right ) y-3 a^{2} x^{3}-2 c \,x^{2}-3 b^{2} x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.594 |
|
|
\[
{}y^{\prime } y = \left (\left (3-m \right ) x -1\right ) y-\left (m -1\right ) a x
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.243 |
|
|
\[
{}y^{\prime } y+x \left (a \,x^{2}+b \right ) y+x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.154 |
|
|
\[
{}y^{\prime } y+a \left (1-\frac {1}{x}\right ) y = a^{2}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.883 |
|
|
\[
{}y^{\prime } y-a \left (1-\frac {b}{x}\right ) y = a^{2} b
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.931 |
|
|
\[
{}y^{\prime } y = x^{n -1} \left (\left (2 n +1\right ) x +a n \right ) y-n \,x^{2 n} \left (x +a \right )
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
2.798 |
|
|
\[
{}y^{\prime } y = a \left (-b n +x \right ) x^{n -1} y+c \left (x^{2}-\left (2 n +1\right ) b x +n \left (n +1\right ) b^{2}\right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
5.530 |
|
|
\[
{}y^{\prime } y = \left (a \left (2 n +k \right ) x^{k}+b \right ) x^{n -1} y+\left (-a^{2} n \,x^{2 k}-a b \,x^{k}+c \right ) x^{2 n -1}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
42.371 |
|
|
\[
{}y^{\prime } y = \left (a \left (2 n +k \right ) x^{2 k}+b \left (2 m -k \right )\right ) x^{m -k -1} y-\frac {a^{2} m \,x^{4 k}+c \,x^{2 k}+b^{2} m}{x}
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
53.830 |
|