| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{3} {y^{\prime }}^{3}&=27 x \left (y^{2}-2 x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.418 |
|
| \begin{align*}
y^{\prime }-8 x \sqrt {y}&=\frac {4 x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.628 |
|
| \begin{align*}
2 x -\ln \left (y+1\right )-\frac {\left (x +y\right ) y^{\prime }}{y+1}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.683 |
|
| \begin{align*}
x y^{\prime }&=\left (x^{2}+\tan \left (y\right )\right ) \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✓ |
✗ |
7.541 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.499 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x^{2}}{1+x^{3}+y} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
3.006 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (y+1\right )^{2}}{x \left (y+1\right )-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.877 |
|
| \begin{align*}
\left (y-2 x y^{\prime }\right )^{2}&=4 y {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
31.641 |
|
| \begin{align*}
6 x^{5} y+\left (y^{4} \ln \left (y\right )-3 x^{6}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.232 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x}}{2}+y^{{1}/{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
12.911 |
|
| \begin{align*}
2 x y^{\prime }+1&=y+\frac {x^{2}}{-1+y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
5.898 |
|
| \begin{align*}
y y^{\prime }+x&=\frac {\left (x^{2}+y^{2}\right )^{2}}{2 x^{2}} \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
6.794 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (3 x +y^{3}-1\right )^{2}}{y^{2}} \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✓ |
16.329 |
|
| \begin{align*}
\left (x \sqrt {1+y^{2}}+1\right ) \left (1+y^{2}\right )&=x y y^{\prime } \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.204 |
|
| \begin{align*}
\left (1+x^{2}+y^{2}\right ) y y^{\prime }+\left (x^{2}+y^{2}-1\right ) x&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.536 |
|
| \begin{align*}
y^{2} \left (x -1\right )&=x \left (y x +x -2 y\right ) y^{\prime } \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
11.883 |
|
| \begin{align*}
\left (x y^{\prime }-y\right )^{2}&=x^{2} y^{2}-x^{4} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
11.392 |
|
| \begin{align*}
x y y^{\prime }-x^{2} \sqrt {1+y^{2}}&=\left (x +1\right ) \left (1+y^{2}\right ) \\
\end{align*} |
[‘x=_G(y,y’)‘] |
✗ |
✓ |
✓ |
✓ |
14.511 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.549 |
|
| \begin{align*}
\tan \left (y\right ) y^{\prime }+4 \cos \left (y\right ) x^{3}&=2 x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
21.314 |
|
| \begin{align*}
\tan \left (y\right ) y^{\prime }+4 \cos \left (y\right ) x^{3}&=2 x \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
19.034 |
|
| \begin{align*}
\left (x +y\right ) \left (-y x +1\right )+\left (x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
5.228 |
|
| \begin{align*}
\left (3 y x +x +y\right ) y+\left (4 y x +x +2 y\right ) x y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
27.272 |
|
| \begin{align*}
x^{2}-1+\left (x^{2} y^{2}+x^{3}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
✓ |
✓ |
✓ |
3.635 |
|
| \begin{align*}
x \left ({y^{\prime }}^{2}+{\mathrm e}^{2 y}\right )&=-2 y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.836 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.735 |
|
| \begin{align*}
y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.302 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.604 |
|
| \begin{align*}
y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.657 |
|
| \begin{align*}
y y^{\prime \prime }+1&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.288 |
|
| \begin{align*}
y^{\prime \prime } \left (1+{\mathrm e}^{x}\right )+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.375 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}-{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.992 |
|
| \begin{align*}
y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
2 y y^{\prime \prime }&={y^{\prime }}^{2}+y^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.219 |
|
| \begin{align*}
{y^{\prime \prime }}^{3}+x y^{\prime \prime }&=2 y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✗ |
5.858 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}+y^{\prime }&=x y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}&=2 \,{\mathrm e}^{-y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.554 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }&={y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.275 |
|
| \begin{align*}
y^{\prime \prime }&={\mathrm e}^{y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
6.216 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime \prime \prime }+{y^{\prime \prime \prime }}^{3}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.560 |
|
| \begin{align*}
2 y^{\prime } \left (y^{\prime \prime }+2\right )&=x {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
y^{4}-y^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
22.477 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\left (3 y-2 y^{\prime }\right ) y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.287 |
|
| \begin{align*}
y^{\prime \prime } \left (2 y^{\prime }+x \right )&=1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.718 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-2 y^{\prime } y^{\prime \prime \prime }+1&=0 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
1.620 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.196 |
|
| \begin{align*}
y y^{\prime \prime }-2 y y^{\prime } \ln \left (y\right )&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.547 |
|
| \begin{align*}
\left (2 y+y^{\prime }\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.404 |
|
| \begin{align*}
x y^{\prime \prime }&=y^{\prime }+x \sin \left (\frac {y^{\prime }}{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
10.520 |
|
| \begin{align*}
y^{\prime \prime \prime } {y^{\prime }}^{2}&={y^{\prime \prime \prime }}^{3} \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \begin{align*}
y y^{\prime \prime }+y&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.062 |
|
| \begin{align*}
x y^{\prime \prime }&=y^{\prime }+x \left ({y^{\prime }}^{2}+x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
0.570 |
|
| \begin{align*}
y^{\prime \prime \prime \prime } x&=1 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.223 |
|
| \begin{align*}
x y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.650 |
|
| \begin{align*}
y^{\prime \prime \prime }&=2 x y^{\prime \prime } \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.564 |
|
| \begin{align*}
y^{\prime \prime \prime \prime } x +y^{\prime \prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
y y^{\prime \prime \prime }&=y^{\prime } y^{\prime \prime } \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✗ |
✓ |
✓ |
✗ |
0.088 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.294 |
|
| \begin{align*}
y y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.257 |
|
| \begin{align*}
5 {y^{\prime \prime \prime }}^{2}-3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.681 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.976 |
|
| \begin{align*}
y^{\prime \prime }&=x y^{\prime }+y+1 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.567 |
|
| \begin{align*}
x y^{\prime \prime }&=2 y y^{\prime }-y^{\prime } \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.229 |
|
| \begin{align*}
-y^{\prime }+x y^{\prime \prime }&=x^{2} y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.354 |
|
| \begin{align*}
x y y^{\prime \prime }-{y^{\prime }}^{2} x&=y y^{\prime } \\
\end{align*} |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.222 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+15 y^{2} \sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.292 |
|
| \begin{align*}
\left (x^{2}+1\right ) \left ({y^{\prime }}^{2}-y y^{\prime \prime }\right )&=x y y^{\prime } \\
\end{align*} |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.898 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y y^{\prime \prime }&=2 y y^{\prime } \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.469 |
|
| \begin{align*}
x^{2} y y^{\prime \prime }&=\left (-x y^{\prime }+y\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.457 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}+\frac {y}{x^{2}}&=\frac {{y^{\prime }}^{2}}{y} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.360 |
|
| \begin{align*}
y \left (x y^{\prime \prime }+y^{\prime }\right )&=x {y^{\prime }}^{2} \left (1-x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.381 |
|
| \begin{align*}
x^{2} y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
✓ |
✓ |
✗ |
0.289 |
|
| \begin{align*}
x^{2} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.429 |
|
| \begin{align*}
x y y^{\prime \prime }&=y^{\prime } \left (y^{\prime }+y\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.347 |
|
| \begin{align*}
4 x^{2} y^{3} y^{\prime \prime }&=x^{2}-y^{4} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.473 |
|
| \begin{align*}
x^{3} y^{\prime \prime }&=\left (-x y^{\prime }+y\right ) \left (y-x y^{\prime }-x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.928 |
|
| \begin{align*}
\frac {y^{2}}{x^{2}}+{y^{\prime }}^{2}&=3 x y^{\prime \prime }+\frac {2 y y^{\prime }}{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.538 |
|
| \begin{align*}
y^{\prime \prime }&=\left (2 y x -\frac {5}{x}\right ) y^{\prime }+4 y^{2}-\frac {4 y}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.437 |
|
| \begin{align*}
x^{2} \left (2 y y^{\prime \prime }-{y^{\prime }}^{2}\right )&=1-2 x y y^{\prime } \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✓ |
✗ |
0.465 |
|
| \begin{align*}
x^{2} \left (y y^{\prime \prime }-{y^{\prime }}^{2}\right )+x y y^{\prime }&=\left (2 x y^{\prime }-3 y\right ) \sqrt {x^{3}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.670 |
|
| \begin{align*}
x^{4} \left ({y^{\prime }}^{2}-2 y y^{\prime \prime }\right )&=4 x^{3} y y^{\prime }+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✓ |
✗ |
0.765 |
|
| \begin{align*}
y y^{\prime }+x y y^{\prime \prime }-{y^{\prime }}^{2} x&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.366 |
|
| \begin{align*}
y^{\prime \prime } \left (3+y {y^{\prime }}^{2}\right )&={y^{\prime }}^{4} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.608 |
|
| \begin{align*}
{y^{\prime \prime }}^{2}-y^{\prime } y^{\prime \prime \prime }&=\frac {{y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.159 |
|
| \begin{align*}
y y^{\prime }+2 x^{2} y^{\prime \prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.442 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
✓ |
✓ |
✗ |
0.359 |
|
| \begin{align*}
2 x y^{2} \left (x y^{\prime \prime }+y^{\prime }\right )+1&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✓ |
✗ |
0.423 |
|
| \begin{align*}
x \left (y^{\prime \prime }+{y^{\prime }}^{2}\right )&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| \begin{align*}
y^{2} \left (y^{\prime } y^{\prime \prime \prime }-2 {y^{\prime \prime }}^{2}\right )&={y^{\prime }}^{4} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.066 |
|
| \begin{align*}
y \left (y^{\prime }+2 x y^{\prime \prime }\right )&={y^{\prime }}^{2} x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
✓ |
✓ |
✗ |
0.346 |
|
| \begin{align*}
y^{\prime \prime }+2 y {y^{\prime }}^{2}&=\left (2 x +\frac {1}{x}\right ) y^{\prime } \\
\end{align*} |
[_Liouville, [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.366 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime \prime }&={y^{\prime \prime }}^{2}+y^{\prime \prime } {y^{\prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_exponential_symmetries], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.466 |
|
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2}+2 x y^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.264 |
|
| \begin{align*}
{y^{\prime \prime }}^{4}&={y^{\prime }}^{5}-y {y^{\prime }}^{3} y^{\prime \prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
1.794 |
|
| \begin{align*}
2 y y^{\prime \prime \prime }&=y^{\prime } \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime } {y^{\prime }}^{2}&=1 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✗ |
✗ |
337.752 |
|
| \begin{align*}
y^{2} y^{\prime \prime \prime }&={y^{\prime }}^{3} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.058 |
|