| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.110 |
|
| \begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.254 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.792 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.739 |
|
| \begin{align*}
2 x^{2} y+{y^{\prime }}^{2}&=x^{3} y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.399 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=3 x y^{\prime }+y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.290 |
|
| \begin{align*}
8 x +1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.984 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.214 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=\left (x +y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.868 |
|
| \begin{align*}
x^{2}-3 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.050 |
|
| \begin{align*}
2 x y^{\prime }+y&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.171 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.951 |
|
| \begin{align*}
x +2 y y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
2 x +{y^{\prime }}^{2} x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.586 |
|
| \begin{align*}
x&=y y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.918 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.719 |
|
| \begin{align*}
y&=y^{\prime } x \left (y^{\prime }+1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}+1&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.263 |
|
| \begin{align*}
{y^{\prime }}^{3}+x y y^{\prime }&=2 y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.636 |
|
| \begin{align*}
\frac {1}{{y^{\prime }}^{2}}+x y^{\prime }&=2 y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
91.718 |
|
| \begin{align*}
y&=y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.571 |
|
| \begin{align*}
-x +y&={y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.177 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.279 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.801 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.036 |
|
| \begin{align*}
y&=x y^{\prime }-x^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
13.421 |
|
| \begin{align*}
5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
4.885 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.669 |
|
| \begin{align*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.307 |
|
| \begin{align*}
{y^{\prime }}^{2}&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.310 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
49.248 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x^{2}&=8 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
47.168 |
|
| \begin{align*}
{y^{\prime }}^{2}+a \,x^{2}+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
84.177 |
|
| \begin{align*}
{y^{\prime }}^{2}&=a^{2} y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
48.301 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y^{\prime }+x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.191 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.746 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.258 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.859 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{\prime }+x -y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.628 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.858 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.163 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.902 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }&=b c \,x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.704 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
113.961 |
|
| \begin{align*}
{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.958 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.816 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.781 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.588 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-a x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.775 |
|
| \begin{align*}
{y^{\prime }}^{2}-a y y^{\prime }-a x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.668 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.307 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
11.352 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.976 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.454 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.737 |
|
| \begin{align*}
{y^{\prime }}^{2}&={\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
6.946 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.231 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
5.427 |
|
| \begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.159 |
|
| \begin{align*}
3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
9.530 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.525 |
|
| \begin{align*}
4 {y^{\prime }}^{2}+2 x \,{\mathrm e}^{-2 y} y^{\prime }-{\mathrm e}^{-2 y}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.658 |
|
| \begin{align*}
4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.409 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.076 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.139 |
|
| \begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.011 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.607 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.909 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.494 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y^{\prime }&=y \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.824 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.977 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.017 |
|
| \begin{align*}
{y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.323 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.888 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.494 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
109.273 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
140.987 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.836 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.711 |
|
| \begin{align*}
{y^{\prime }}^{2} x -\left (3 x -y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.473 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.837 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
115.454 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
5.905 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.281 |
|
| \begin{align*}
{y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.879 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a y y^{\prime }+b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.047 |
|
| \begin{align*}
\left (x +1\right ) {y^{\prime }}^{2}&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.433 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.694 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.881 |
|
| \begin{align*}
\left (5+3 x \right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.448 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.506 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
47.369 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +4 y y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
139.098 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.512 |
|
| \begin{align*}
4 \left (2-x \right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.631 |
|
| \begin{align*}
16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.651 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+2 a x y^{\prime }+a^{2}+x^{2}-2 a y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.419 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.934 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.271 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+b^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.779 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=b^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.782 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.849 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.937 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
35.345 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.336 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.006 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.266 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-y x -y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.257 |
|
| \begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.449 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.743 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.297 |
|
| \begin{align*}
y {y^{\prime }}^{2}&=a^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.418 |
|
| \begin{align*}
y {y^{\prime }}^{2}&={\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
20.270 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 a x y^{\prime }-a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.316 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.589 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.172 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.619 |
|
| \begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.651 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.529 |
|
| \begin{align*}
y {y^{\prime }}^{2}+y&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.421 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.652 |
|
| \begin{align*}
\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.314 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.227 |
|
| \begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.264 |
|
| \begin{align*}
\left (1-a y\right ) {y^{\prime }}^{2}&=a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.937 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.271 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.867 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+2 x y y^{\prime }+a -y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.952 |
|
| \begin{align*}
9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.731 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
11.628 |
|
| \begin{align*}
2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.960 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.065 |
|
| \begin{align*}
3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
6.739 |
|
| \begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.363 |
|
| \begin{align*}
{y^{\prime }}^{3}&=b x +a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \begin{align*}
{y^{\prime }}^{3}+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.332 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }+a -b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.658 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
107.199 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
13.579 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
3.364 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
104.464 |
|
| \begin{align*}
{y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.931 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.415 |
|
| \begin{align*}
{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
12.476 |
|
| \begin{align*}
{y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
33.454 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.763 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
12.322 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
1.733 |
|
| \begin{align*}
3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.268 |
|
| \begin{align*}
4 {y^{\prime }}^{3}+4 y^{\prime }&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2}&=27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.033 |
|
| \begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.328 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.251 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.503 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.451 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{3}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
2.274 |
|
| \begin{align*}
y {y^{\prime }}^{3}-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.464 |
|
| \begin{align*}
2 y {y^{\prime }}^{3}-3 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
30.641 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
3.974 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.488 |
|
| \begin{align*}
16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.464 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.011 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime }&=y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
33.154 |
|
| \begin{align*}
\sqrt {1+{y^{\prime }}^{2}}&=x y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.854 |
|
| \begin{align*}
\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right )&=y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
10.381 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.205 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1-x}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.253 |
|
| \begin{align*}
{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.135 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.723 |
|
| \begin{align*}
x&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.940 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
52.586 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.085 |
|
| \begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.093 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=\frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.401 |
|
| \begin{align*}
y y^{\prime }&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.089 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.301 |
|
| \begin{align*}
y-2 x y^{\prime }&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.846 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.223 |
|
| \begin{align*}
\left (-x^{2}+1\right ) {y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.271 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \begin{align*}
8 y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.073 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.935 |
|
| \begin{align*}
16 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.969 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.724 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.772 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.290 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.415 |
|
| \begin{align*}
y {y^{\prime }}^{2}-x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.689 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.901 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.908 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.887 |
|
| \begin{align*}
2 y&={y^{\prime }}^{2}+4 x y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.574 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x^{4} y^{\prime }+8 x^{3} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.643 |
|
| \begin{align*}
{y^{\prime }}^{2}&=4 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.587 |
|
| \begin{align*}
1+{x^{\prime }}^{2}&=\frac {a}{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.621 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.473 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.553 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.698 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.212 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.616 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
2.527 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
73.093 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.984 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.652 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.168 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.057 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.766 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.419 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.872 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.135 |
|
| \begin{align*}
y&=x^{6} {y^{\prime }}^{3}-x y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.169 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.613 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.645 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.442 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
2.511 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
45.684 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.448 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.716 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.642 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.637 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.641 |
|
| \begin{align*}
y&=x y^{\prime }+x^{3} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
22.909 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.652 |
|
| \begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.701 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.539 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.571 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.568 |
|
| \begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
4.796 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.204 |
|
| \begin{align*}
16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.327 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}&=8 x y^{\prime }+16 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.731 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
26.695 |
|
| \begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.026 |
|
| \begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.643 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \begin{align*}
{y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.336 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.657 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.021 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {y^{3}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
10.283 |
|
| \begin{align*}
{y^{\prime }}^{3}&=\frac {y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
79.026 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{y x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
16.381 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
13.224 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
66.390 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.720 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.504 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
81.808 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
14.286 |
|
| \begin{align*}
{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.190 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.918 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
62.069 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.793 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.440 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.733 |
|
| \begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| \begin{align*}
3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.720 |
|
| \begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
19.558 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.269 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.416 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.654 |
|
| \begin{align*}
{y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.868 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.137 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
12.714 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
92.369 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \begin{align*}
{y^{\prime }}^{2} x +\left (y-3 x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.584 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }+a y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.150 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
90.088 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.398 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.847 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.104 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.163 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a y y^{\prime }+b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.455 |
|
| \begin{align*}
\left (x y^{\prime }+a \right )^{2}-2 a y+x^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.125 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.398 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
0.997 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.927 |
|
| \begin{align*}
{\mathrm e}^{-2 x} {y^{\prime }}^{2}-\left (y^{\prime }-1\right )^{2}+{\mathrm e}^{-2 y}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.182 |
|
| \begin{align*}
y {y^{\prime }}^{2}-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
y {y^{\prime }}^{2}-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.630 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.634 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.667 |
|
| \begin{align*}
y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+a^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.902 |
|
| \begin{align*}
y {y^{\prime }}^{2}+a x y^{\prime }+b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
y {y^{\prime }}^{2}+x^{3} y^{\prime }-x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.852 |
|
| \begin{align*}
\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \begin{align*}
\left (y-2 x \right ) {y^{\prime }}^{2}-2 \left (x -1\right ) y^{\prime }+y-2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.873 |
|
| \begin{align*}
2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.804 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.498 |
|
| \begin{align*}
9 y {y^{\prime }}^{2}+4 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.258 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.632 |
|
| \begin{align*}
\left (b +a y\right ) \left (1+{y^{\prime }}^{2}\right )-c&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.347 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-4 a y y^{\prime }+4 a^{2}-4 a x +y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.833 |
|
| \begin{align*}
\left (y^{2}-2 a x +a^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
2.604 |
|
| \begin{align*}
\left (3 y-2\right ) {y^{\prime }}^{2}-4+4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \begin{align*}
\sin \left (y\right ) {y^{\prime }}^{2}+2 x y^{\prime } \cos \left (y\right )^{3}-\sin \left (y\right ) \cos \left (y\right )^{4}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✗ |
✓ |
✗ |
11.135 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (a \cos \left (y\right )+b \right )-c \cos \left (y\right )+d&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.811 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
79.302 |
|
| \begin{align*}
{y^{\prime }}^{2}-a x y y^{\prime }+2 a y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.411 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{4} y^{\prime }-y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.845 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.173 |
|
| \begin{align*}
4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.290 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.158 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.704 |
|
| \begin{align*}
16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.656 |
|
| \begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.604 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.369 |
|
| \begin{align*}
\left (x^{2}+1\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| \begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.588 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.659 |
|
| \begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
6.531 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.886 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.201 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.127 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 x y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.159 |
|
| \begin{align*}
4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.445 |
|
| \begin{align*}
{\mathrm e}^{2 y} {y^{\prime }}^{3}+\left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
31.868 |
|
| \begin{align*}
x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
7.089 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.177 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.730 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.851 |
|
| \begin{align*}
y&=\left (x +1\right ) {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.446 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {y {y^{\prime }}^{2}}{x^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.264 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.292 |
|
| \begin{align*}
8 \left (y^{\prime }+1\right )^{3}&=27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
22.626 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.034 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.474 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.139 |
|
| \begin{align*}
x&={y^{\prime }}^{3}-y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.946 |
|
| \begin{align*}
y&=5 x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.519 |
|
| \begin{align*}
y&=x^{2}+2 x y^{\prime }+\frac {{y^{\prime }}^{2}}{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
5.699 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.048 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.408 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.011 |
|
| \begin{align*}
\sinh \left (x \right ) {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
37.488 |
|
| \begin{align*}
{y^{\prime }}^{2} \sqrt {y}&=\sin \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
18.192 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.348 |
|
| \begin{align*}
y&=2 x y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.847 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.054 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.750 |
|
| \begin{align*}
y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.329 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.262 |
|
| \begin{align*}
{y^{\prime }}^{2}-9 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
10.547 |
|
| \begin{align*}
{y^{\prime }}^{2}+y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.816 |
|
| \begin{align*}
y&=t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.129 |
|
| \begin{align*}
y&=t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.098 |
|
| \begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.821 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{2 x}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.619 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
428.332 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.378 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 x y^{\prime }+2 y+2 x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
3.856 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.675 |
|
| \begin{align*}
x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \begin{align*}
{y^{\prime }}^{2} x&={\mathrm e}^{\frac {1}{y^{\prime }}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.888 |
|
| \begin{align*}
x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.914 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.928 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
109.871 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )-4 y y^{\prime }-4 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.905 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.250 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.086 |
|
| \begin{align*}
8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2}&=-27 x +27 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.567 |
|
| \begin{align*}
y&={y^{\prime }}^{2}-x y^{\prime }+x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.474 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.375 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.109 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.136 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.321 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=y^{\prime }+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.086 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \alpha \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y&=2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
2.109 |
|
| \begin{align*}
x&=y y^{\prime }+a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.192 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +{y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
69.066 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.717 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.096 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.629 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}-2 x y y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.532 |
|
| \begin{align*}
y&=2 x y^{\prime }+\frac {x^{2}}{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
2.246 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.624 |
|
| \begin{align*}
x y^{\prime }+y&=x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.323 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.835 |
|
| \begin{align*}
{y^{\prime }}^{2} \left (x^{2}-1\right )&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y-2 x y^{\prime }-y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.172 |
|
| \begin{align*}
x&={y^{\prime }}^{2}+y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.896 |
|
| \begin{align*}
{y^{\prime }}^{2}-a \,x^{3}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.760 |
|
| \begin{align*}
{y^{\prime }}^{3}&=a \,x^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| \begin{align*}
x -y y^{\prime }&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
58.990 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.029 |
|
| \begin{align*}
y&=2 y^{\prime }+3 {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.693 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.336 |
|
| \begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.450 |
|
| \begin{align*}
y&=y {y^{\prime }}^{2}+2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.069 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.732 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.862 |
|
| \begin{align*}
{\mathrm e}^{4 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.483 |
|
| \begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.986 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.705 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.183 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.562 |
|
| \begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
86.372 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.621 |
|
| \begin{align*}
\left (y^{\prime }+1\right )^{3}&=\frac {7 \left (x +y\right ) \left (1-y^{\prime }\right )^{3}}{4 a} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.838 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.592 |
|
| \begin{align*}
a {y^{\prime }}^{3}&=27 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.444 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
1.073 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.620 |
|
| \begin{align*}
\left (8 {y^{\prime }}^{3}-27\right ) x&=12 y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| \begin{align*}
{x^{\prime }}^{2}&=k^{2} \left (1-{\mathrm e}^{-\frac {2 g x}{k^{2}}}\right ) \\
x \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
4.583 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.510 |
|
| \begin{align*}
{y^{\prime }}^{3}-a \,x^{4}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.990 |
|
| \begin{align*}
{y^{\prime }}^{2}-y y^{\prime }+x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.973 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x +y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.792 |
|
| \begin{align*}
{y^{\prime }}^{2} x +a x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.811 |
|
| \begin{align*}
{y^{\prime }}^{3}+y^{\prime }&={\mathrm e}^{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
5.104 |
|
| \begin{align*}
y&=\ln \left (\cos \left (y^{\prime }\right )\right )+y^{\prime } \tan \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.243 |
|
| \begin{align*}
x&=y y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.518 |
|
| \begin{align*}
\left (2 x -b \right ) y^{\prime }&=y-a y {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.181 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.661 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.341 |
|
| \begin{align*}
x^{2}&=a^{2} \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.552 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.350 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.662 |
|
| \begin{align*}
x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.361 |
|
| \begin{align*}
y&=\frac {2 a {y^{\prime }}^{2}}{\left (1+{y^{\prime }}^{2}\right )^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.546 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +4 y y^{\prime }&=y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
1.758 |
|
| \begin{align*}
a^{2} y {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.566 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.332 |
|
| \begin{align*}
y y^{\prime }+x&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.375 |
|
| \begin{align*}
2 y&=x y^{\prime }+\frac {a}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.319 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.930 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✗ |
✓ |
1.922 |
|
| \begin{align*}
4 {y^{\prime }}^{2}&=9 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.928 |
|
| \begin{align*}
3 y&=2 x y^{\prime }-\frac {2 {y^{\prime }}^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.049 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x&=\left (3 x -1\right )^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.102 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \begin{align*}
3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x^{3} y^{\prime }-4 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.434 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.511 |
|
| \begin{align*}
x^{2}+y&={y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
15.877 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y^{4} \left (x y^{\prime }+y\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.950 |
|
| \begin{align*}
\left (1-y^{\prime }\right )^{2}-{\mathrm e}^{-2 y}&={\mathrm e}^{-2 x} {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.783 |
|
| \begin{align*}
8 x {y^{\prime }}^{3}&=y \left (12 {y^{\prime }}^{2}-9\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| \begin{align*}
y&=\frac {x}{y^{\prime }}-a y^{\prime } \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
72.451 |
|
| \begin{align*}
x {y^{\prime }}^{3}&=a +b y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.994 |
|
| \begin{align*}
a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.901 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.295 |
|
| \begin{align*}
{\mathrm e}^{3 x} \left (y^{\prime }-1\right )+{\mathrm e}^{2 y} {y^{\prime }}^{3}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
96.226 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.613 |
|
| \begin{align*}
y&=-x y^{\prime }+x^{4} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.240 |
|
| \begin{align*}
y-2 x y^{\prime }+a y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \begin{align*}
x^{2} \left (-x y^{\prime }+y\right )&=y {y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.572 |
|
| \begin{align*}
{y^{\prime }}^{3}-4 x y y^{\prime }+8 y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.603 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.158 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+a^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.789 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
{x^{\prime }}^{2}&=-4 x+4 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.646 |
|
| \begin{align*}
{x^{\prime }}^{2}-x t +x&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.639 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) \left (1+{y^{\prime }}^{2}\right )+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.125 |
|
| \begin{align*}
y-\frac {x y^{\prime }}{2}-\frac {x}{2 y^{\prime }}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.861 |
|
| \begin{align*}
x&=y-{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
y&=2 x y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.504 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \begin{align*}
{y^{\prime }}^{2} x -3 y y^{\prime }+9 x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
5.237 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 y y^{\prime }-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.974 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+3 {y^{\prime }}^{2}&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.447 |
|
| \begin{align*}
2 a \,x^{3} y-a \,x^{2} y^{\prime }+c {y^{\prime }}^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.928 |
|
| \begin{align*}
x +y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.760 |
|
| \begin{align*}
2 x +y y^{\prime } \left (4 {y^{\prime }}^{2}+6\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
4.664 |
|
| \begin{align*}
y&=4 {y^{\prime }}^{2} x +2 x y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.286 |
|
| \begin{align*}
y-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.691 |
|
| \begin{align*}
{b^{\prime }}^{7}&=3 p \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.191 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
218.561 |
|
| \begin{align*}
y&=\tan \left (x \right ) y^{\prime }-{y^{\prime }}^{2} \sec \left (x \right )^{2} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.879 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (3 y-2 x \right ) y^{\prime }-6 y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
56.033 |
|
| \begin{align*}
{\mathrm e}^{x} {y^{\prime }}^{2}+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.662 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.962 |
|
| \begin{align*}
{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.900 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.237 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.914 |
|
| \begin{align*}
{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
68.927 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.255 |
|
| \begin{align*}
{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.526 |
|
| \begin{align*}
2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.118 |
|
| \begin{align*}
x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.704 |
|
| \begin{align*}
x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
1.300 |
|
| \begin{align*}
4 x -2 y y^{\prime }+{y^{\prime }}^{2} x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.442 |
|
| \begin{align*}
3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.088 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.890 |
|
| \begin{align*}
y&=x^{6} {y^{\prime }}^{3}-x y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.931 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.923 |
|
| \begin{align*}
2 {y^{\prime }}^{3}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
7.058 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.993 |
|
| \begin{align*}
{y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.899 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x -3 y y^{\prime }+3&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
46.932 |
|
| \begin{align*}
{y^{\prime }}^{3}-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.102 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.269 |
|
| \begin{align*}
2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.538 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.278 |
|
| \begin{align*}
{y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.289 |
|
| \begin{align*}
y&=x y^{\prime }+x^{3} {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
19.255 |
|
| \begin{align*}
8 y&={y^{\prime }}^{2}+3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
26.888 |
|
| \begin{align*}
{y^{\prime }}^{2} x +y y^{\prime }&=3 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.786 |
|
| \begin{align*}
9 {y^{\prime }}^{2} x +3 y y^{\prime }+y^{8}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
3.589 |
|
| \begin{align*}
{y^{\prime }}^{2}+x y^{2} y^{\prime }+y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.451 |
|
| \begin{align*}
4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.588 |
|
| \begin{align*}
4 y {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.220 |
|
| \begin{align*}
9 {y^{\prime }}^{2}+12 x y^{4} y^{\prime }+4 y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.181 |
|
| \begin{align*}
2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.984 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{3} y^{\prime }+y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.076 |
|
| \begin{align*}
9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
0.977 |
|
| \begin{align*}
y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.161 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.421 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{3}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
2.296 |
|
| \begin{align*}
y {y^{\prime }}^{2}-x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.795 |
|
| \begin{align*}
y {y^{\prime }}^{3}-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.774 |
|
| \begin{align*}
x^{3} {y^{\prime }}^{2}+x^{2} y y^{\prime }+4&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.478 |
|
| \begin{align*}
9 {y^{\prime }}^{2}+3 x y^{4} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.178 |
|
| \begin{align*}
4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
1.161 |
|
| \begin{align*}
x^{6} {y^{\prime }}^{2}-2 x y^{\prime }-4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.734 |
|
| \begin{align*}
5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.959 |
|
| \begin{align*}
4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
3.596 |
|
| \begin{align*}
4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.951 |
|
| \begin{align*}
16 {y^{\prime }}^{2} x +8 y y^{\prime }+y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✗ |
2.145 |
|
| \begin{align*}
{y^{\prime }}^{3}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.868 |
|
| \begin{align*}
9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
3.782 |
|
| \begin{align*}
x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.839 |
|
| \begin{align*}
y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.113 |
|
| \begin{align*}
{y^{\prime }}^{2}+y y^{\prime }-x -1&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.148 |
|
| \begin{align*}
{y^{\prime }}^{3}&=a \,x^{4} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.632 |
|
| \begin{align*}
y {y^{\prime }}^{2}+2 x y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
\left (-x y^{\prime }+y\right )^{2}&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.296 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{x}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.613 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
223.964 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
{y^{\prime }}^{2} x&={\mathrm e}^{\frac {1}{y^{\prime }}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.617 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
94.456 |
|
| \begin{align*}
8 {y^{\prime }}^{3}&=27 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.947 |
|
| \begin{align*}
y {y^{\prime }}^{3}+x&=1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.551 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.524 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y \left (2 y^{\prime }-1\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.652 |
|
| \begin{align*}
{y^{\prime }}^{2}+x&=2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.907 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
229.930 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{x}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.320 |
|
| \begin{align*}
x&={y^{\prime }}^{3}+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.771 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
y&={y^{\prime }}^{2}+2 {y^{\prime }}^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
0.913 |
|
| \begin{align*}
y&=\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.664 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }&=x^{2}-4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
10.316 |
|
| \begin{align*}
5 y+{y^{\prime }}^{2}&=x \left (x +y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
6.070 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}&=x y y^{\prime }+1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \begin{align*}
y&=x y^{\prime }-x^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
13.987 |
|
| \begin{align*}
y&=2 x y^{\prime }+y^{2} {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.013 |
|
| \begin{align*}
x y^{\prime }+y&=4 \sqrt {y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
182.532 |
|
| \begin{align*}
y&=3 x y^{\prime }-7 {y^{\prime }}^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
9.090 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.136 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -2 {y^{\prime }}^{3} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
52.640 |
|
| \begin{align*}
x y^{\prime } \left (y^{\prime }+2\right )&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.135 |
|
| \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*}
2 {y^{\prime }}^{3}-3 {y^{\prime }}^{2}+x&=y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✗ |
✗ |
1.293 |
|
| \begin{align*}
3 {y^{\prime }}^{3}-x y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.217 |
|
| \begin{align*}
{y^{\prime }}^{2} x&=y-y^{\prime } \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.012 |
|
| \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 }}^{3}+\left (-2 y^{\prime }+{y^{\prime }}^{2}\right ) x&=3 y^{\prime }-y \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
60.621 |
|
| \begin{align*}
y&=y^{\prime } \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.944 |
|
| \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*}
x \left ({y^{\prime }}^{2}+{\mathrm e}^{2 y}\right )&=-2 y^{\prime } \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.836 |
|