| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y&={y^{\prime }}^{2} x -2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.640 |
|
| \begin{align*}
x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
12.995 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \begin{align*}
2 {y^{\prime }}^{2} \left (-x y^{\prime }+y\right )&=1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.280 |
|
| \begin{align*}
2 x y^{\prime }-y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
53.631 |
|
| \begin{align*}
{y^{\prime }}^{3}&=3 x y^{\prime }-3 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.784 |
|
| \begin{align*}
x y^{\prime }+x^{2}+y x -y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.932 |
|
| \begin{align*}
2 x y^{\prime }+y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.702 |
|
| \begin{align*}
2 x y^{2}-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.323 |
|
| \begin{align*}
\left (x y^{\prime }+y\right )^{2}&=x^{2} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
y-y^{\prime }&=x y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.337 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
12.625 |
|
| \begin{align*}
{y^{\prime }}^{3}-{\mathrm e}^{2 x} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.706 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.305 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 \left (x -1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.507 |
|
| \begin{align*}
y+y^{\prime } \ln \left (y\right )^{2}&=\left (x +2 \ln \left (y\right )\right ) y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.962 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x&=3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.474 |
|
| \begin{align*}
y y^{\prime }+x&=y^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.441 |
|
| \begin{align*}
y&=\left (x y^{\prime }+2 y\right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.282 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.373 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (3 x -6\right ) y^{\prime }&=3 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.868 |
|
| \begin{align*}
x -\frac {y}{y^{\prime }}&=\frac {2}{y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
94.040 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.293 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
151.775 |
|
| \begin{align*}
2 x^{3} y y^{\prime }+3 x^{2} y^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.649 |
|
| \begin{align*}
\frac {1}{x}&=\left (\frac {1}{y}-2 x \right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
47.875 |
|
| \begin{align*}
x y^{\prime }&={\mathrm e}^{y}+2 y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.757 |
|
| \begin{align*}
2 \left (x -y^{2}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.721 |
|
| \begin{align*}
y^{\prime }+y x -x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.389 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{2} \left (2 x y^{\prime }-y\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.921 |
|
| \begin{align*}
\frac {-x y^{\prime }+y}{y y^{\prime }+x}&=2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.676 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+2 y x&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.636 |
|
| \begin{align*}
x y \left (x y^{\prime }-y\right )^{2}+2 y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.263 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.262 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.539 |
|
| \begin{align*}
x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.655 |
|
| \begin{align*}
\left (\sin \left (x \right )+y\right ) y^{\prime }+\cos \left (x \right ) y-x^{2}&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
9.803 |
|
| \begin{align*}
3 {y^{\prime }}^{3}-x y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
y y^{\prime }+y^{2} \cot \left (x \right )&=\cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.221 |
|
| \begin{align*}
{\mathrm e}^{y}+2 y x +\left (x +{\mathrm e}^{y}\right ) x y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.775 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y-y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.012 |
|
| \begin{align*}
x \left (x +1\right ) \left (y^{\prime }-1\right )&=y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.631 |
|
| \begin{align*}
y \left (-x y^{\prime }+y\right )&=\sqrt {y^{4}+x^{4}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.915 |
|
| \begin{align*}
x y^{\prime }+y&=\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
79.418 |
|
| \begin{align*}
x^{2} \left (y^{\prime }-1\right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.744 |
|
| \begin{align*}
y^{\prime }+x y^{{1}/{3}}&=3 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.929 |
|
| \begin{align*}
\left (x \cos \left (y\right )+\sin \left (2 y\right )\right ) y^{\prime }&=1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.858 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.017 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.359 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.534 |
|
| \begin{align*}
\left (4 y x -3\right ) y^{\prime }+y^{2}&=1 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
30.569 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {-x +y}+\sqrt {x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.358 |
|
| \begin{align*}
x y^{\prime }&=2 \sqrt {y}\, \cos \left (x \right )-2 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.623 |
|
| \begin{align*}
3 {y^{\prime }}^{4}&=y^{\prime }+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
573.396 |
|
| \begin{align*}
y^{2} \left (-x y^{\prime }+y\right )&=x^{3} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.305 |
|
| \begin{align*}
y^{\prime }&=\left (4 x +y-3\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
13.030 |
|
| \begin{align*}
\left (\cos \left (x \right )-x \sin \left (x \right )\right ) y+\left (x \cos \left (x \right )-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
14.710 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.118 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 x y \ln \left (x \right )+1&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.520 |
|
| \begin{align*}
x y^{\prime }&=x \sqrt {y-x^{2}}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.907 |
|
| \begin{align*}
\left (2 x \,{\mathrm e}^{y}+y^{4}\right ) y^{\prime }&=y \,{\mathrm e}^{y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
6.115 |
|
| \begin{align*}
x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
48.231 |
|
| \begin{align*}
2 y^{\prime }&=x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.974 |
|
| \begin{align*}
\left (2 x^{2} y-3 y^{2}\right ) y^{\prime }&=6 x^{2}-2 x y^{2}+1 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.799 |
|
| \begin{align*}
y y^{\prime }&=4 x +3 y-2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.055 |
|
| \begin{align*}
y^{2} y^{\prime }+x^{2} \sin \left (x \right )^{3}&=y^{3} \cot \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.934 |
|
| \begin{align*}
2 x y^{\prime }-y&=\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.869 |
|
| \begin{align*}
\left (y x -1\right )^{2} x y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.102 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y \sin \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.178 |
|
| \begin{align*}
x y^{\prime }-y&=x \sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.425 |
|
| \begin{align*}
y^{2}+x^{2} {y^{\prime }}^{5}&=x y \left ({y^{\prime }}^{2}+{y^{\prime }}^{3}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.825 |
|
| \begin{align*}
y^{\prime }&=\left (2 x -y\right )^{{1}/{3}}+2 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.047 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.211 |
|
| \begin{align*}
2 x^{2} y+2 \sqrt {1+y^{2} x^{4}}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
15.959 |
|
| \begin{align*}
\left (y^{\prime }-x \sqrt {y}\right ) \left (x^{2}-1\right )&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.374 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (-2 y^{\prime }+{y^{\prime }}^{2}\right ) x&=3 y^{\prime }-y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
60.621 |
|
| \begin{align*}
2 x +3 y-1+\left (4 x +6 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.722 |
|
| \begin{align*}
2 x y^{2}-y+\left (y^{2}+x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.770 |
|
| \begin{align*}
y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.944 |
|
| \begin{align*}
y^{2}&=\left (x y y^{\prime }+1\right ) \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.666 |
|
| \begin{align*}
4 y&={y^{\prime }}^{2}+x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
27.164 |
|
| \begin{align*}
2 x y^{\prime }+y+x y^{2} \left (x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.570 |
|
| \begin{align*}
x +\left (\cot \left (y\right ) x^{2}-3 \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.449 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 \left (y x -2\right ) y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.939 |
|
| \begin{align*}
x y^{\prime }+1&={\mathrm e}^{x -y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.350 |
|
| \begin{align*}
y^{\prime }&=-\tan \left (2 x -y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.287 |
|
| \begin{align*}
3 x^{2}-y&=\sqrt {x^{2}+1}\, y^{\prime } \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \begin{align*}
y y^{\prime }+y x&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.792 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+y^{3}&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.735 |
|
| \begin{align*}
x y^{\prime }&=2 y+\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
676.727 |
|
| \begin{align*}
\left (2 x +y+5\right ) y^{\prime }&=3 x +6 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
625.926 |
|
| \begin{align*}
y^{\prime }+\tan \left (y\right )&=x \sec \left (y\right ) \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
5.322 |
|
| \begin{align*}
{y^{\prime }}^{4}&=4 y \left (x y^{\prime }-2 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
178.191 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-x}{2 \left (x +1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
✓ |
2.955 |
|
| \begin{align*}
x y^{\prime }&=x^{2} {\mathrm e}^{-y}+2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.958 |
|
| \begin{align*}
y^{\prime }&=3 x +\sqrt {y-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
127.893 |
|
| \begin{align*}
x y^{\prime }-2 y+x y^{2} \left (2 x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.717 |
|
| \begin{align*}
x^{3}-2 x y^{2}+3 x^{2} y y^{\prime }&=x y^{\prime }-y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
49.469 |
|