Number of problems in this table is 1193
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.319 |
|
|
\[ {}\left (3 x -y\right ) y^{\prime } = 3 y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.332 |
|
|
\[ {}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.339 |
|
|
\[ {}\sin \left (\frac {y}{x}\right ) \left (-y+x y^{\prime }\right ) = x \cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.664 |
|
|
\[ {}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.809 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {9 x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.483 |
|
|
\[ {}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
[_separable] |
✓ |
✓ |
0.135 |
|
|
\[ {}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.69 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.586 |
|
|
\[ {}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
0.325 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+3 x y+x^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.296 |
|
|
\[ {}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.119 |
|
|
\[ {}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.352 |
|
|
\[ {}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.881 |
|
|
\[ {}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime } = \frac {4 y-2 x}{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.953 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.803 |
|
|
\[ {}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.087 |
|
|
\[ {}y^{\prime } = \frac {a y+x}{x a -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.393 |
|
|
\[ {}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.944 |
|
|
\[ {}\left (2 y-x \right ) y^{\prime } = y+2 x \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.664 |
|
|
\[ {}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{3}+x^{3} = 3 x y^{2} y^{\prime } \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.616 |
|
|
\[ {}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.642 |
|
|
\[ {}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.565 |
|
|
\[ {}x -y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.62 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.435 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.681 |
|
|
\[ {}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.096 |
|
|
\[ {}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.381 |
|
|
\[ {}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.677 |
|
|
\[ {}x y^{\prime } = y \cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.194 |
|
|
\[ {}y+\sqrt {x y}-x y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.49 |
|
|
\[ {}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.134 |
|
|
\[ {}x +y-\left (x -y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.603 |
|
|
\[ {}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.068 |
|
|
\[ {}-y+x y^{\prime } = y y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.436 |
|
|
\[ {}x^{2}+x y+y^{2} = x^{2} y^{\prime } \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.477 |
|
|
\[ {}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
12.835 |
|
|
\[ {}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}} \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime } = \frac {x}{y}+\frac {y}{x} \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.636 |
|
|
\[ {}x y^{\prime } = y+\sqrt {-x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.382 |
|
|
\[ {}y+\left (2 \sqrt {x y}-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.884 |
|
|
\[ {}x y^{\prime } = y \ln \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.492 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \] |
2 |
2 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.827 |
|
|
\[ {}{y^{\prime }}^{2} x^{2}-3 x y y^{\prime }+2 y^{2} = 0 \] |
2 |
2 |
2 |
[_separable] |
✓ |
✓ |
0.859 |
|
|
\[ {}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.688 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
2 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.971 |
|
|
\[ {}y^{\prime }+\frac {2 y+x}{x} = 0 \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
0.663 |
|
|
\[ {}y^{\prime } = \frac {y}{x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.464 |
|
|
\[ {}x y^{\prime } = x +\frac {y}{2} \] |
1 |
0 |
1 |
[_linear] |
✗ |
N/A |
0.697 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.71 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x y+x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.534 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.552 |
|
|
\[ {}y^{\prime } = \frac {y+x \,{\mathrm e}^{-\frac {2 y}{x}}}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.418 |
|
|
\[ {}x^{2}-2 y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.757 |
|
|
\[ {}x^{2} y^{\prime }-3 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.941 |
|
|
\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.297 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.29 |
|
|
\[ {}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.743 |
|
|
\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.356 |
|
|
\[ {}x y^{\prime } = 2 x -6 y \] |
1 |
1 |
1 |
[_linear] |
✓ |
✓ |
1.391 |
|
|
\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.622 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+2 x y \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.885 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.695 |
|
|
\[ {}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.257 |
|
|
\[ {}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.097 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.489 |
|
|
\[ {}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.023 |
|
|
|
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