Number of problems in this table is 256
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime } \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.832 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }+2 y^{2} = x^{2} \] |
2 |
6 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.738 |
|
|
\[ {}y = y^{\prime } x \left (y^{\prime }+1\right ) \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.954 |
|
|
\[ {}y = x +3 \ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[_separable] |
✓ |
✓ |
3.73 |
|
|
\[ {}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.189 |
|
|
\[ {}x \left ({y^{\prime }}^{2}-1\right ) = 2 y y^{\prime } \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.735 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.728 |
|
|
\[ {}y {y^{\prime }}^{2} = 3 x y^{\prime }+y \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.712 |
|
|
\[ {}8 x +1 = y {y^{\prime }}^{2} \] |
2 |
5 |
2 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
3.06 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) x = \left (x +y\right ) y^{\prime } \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.98 |
|
|
\[ {}y+2 x y^{\prime } = {y^{\prime }}^{2} x \] |
2 |
4 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.326 |
|
|
\[ {}x = y-{y^{\prime }}^{3} \] |
3 |
4 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.114 |
|
|
\[ {}x +2 y y^{\prime } = {y^{\prime }}^{2} x \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.735 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.733 |
|
|
\[ {}x {y^{\prime }}^{3} = y y^{\prime }+1 \] |
3 |
4 |
3 |
[_dAlembert] |
✓ |
✓ |
152.212 |
|
|
\[ {}y \left (1+{y^{\prime }}^{2}\right ) = 2 x y^{\prime } \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.17 |
|
|
\[ {}2 x +{y^{\prime }}^{2} x = 2 y y^{\prime } \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.827 |
|
|
\[ {}x = y y^{\prime }+{y^{\prime }}^{2} \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
1.601 |
|
|
\[ {}4 {y^{\prime }}^{2} x +2 x y^{\prime } = y \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.678 |
|
|
\[ {}y = y^{\prime } x \left (y^{\prime }+1\right ) \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.906 |
|
|
\[ {}2 x {y^{\prime }}^{3}+1 = y {y^{\prime }}^{2} \] |
3 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
32.186 |
|
|
\[ {}3 {y^{\prime }}^{4} x = {y^{\prime }}^{3} y+1 \] |
4 |
1 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.234 |
|
|
\[ {}2 {y^{\prime }}^{5}+2 x y^{\prime } = y \] |
5 |
2 |
6 |
[_dAlembert] |
✓ |
✓ |
0.499 |
|
|
\[ {}\frac {1}{{y^{\prime }}^{2}}+x y^{\prime } = 2 y \] |
3 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
111.202 |
|
|
\[ {}2 y = 3 x y^{\prime }+4+2 \ln \left (y^{\prime }\right ) \] |
0 |
2 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.101 |
|
|
\[ {}y-x = {y^{\prime }}^{2} \left (1-\frac {2 y^{\prime }}{3}\right ) \] |
3 |
3 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.214 |
|
|
\[ {}x +y+\left (x -y\right ) y^{\prime } = 0 \] |
1 |
3 |
2 |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.664 |
|
|
\[ {}x y^{\prime } \left (y^{\prime }+2\right ) = y \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.412 |
|
|
\[ {}x y^{\prime }+y = 4 \sqrt {y^{\prime }} \] |
2 |
3 |
2 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
11.989 |
|
|
\[ {}2 x y^{\prime }-y = \ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.606 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {x y^{\prime }}{y}} \] |
0 |
2 |
1 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.599 |
|
|
\[ {}{y^{\prime }}^{2} = x -y \] |
2 |
2 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.408 |
|
|
\[ {}{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right ) = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.232 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.34 |
|
|
\[ {}{y^{\prime }}^{2}+x y^{\prime }+x -y = 0 \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.307 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.315 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.279 |
|
|
\[ {}{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y = 0 \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.299 |
|
|
\[ {}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.36 |
|
|
\[ {}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
0.417 |
|
|
\[ {}{y^{\prime }}^{2}+a y y^{\prime }-x a = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
0.776 |
|
|
\[ {}{y^{\prime }}^{2}-a y y^{\prime }-x a = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
0.467 |
|
|
\[ {}{y^{\prime }}^{2} = {\mathrm e}^{4 x -2 y} \left (y^{\prime }-1\right ) \] |
2 |
2 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.48 |
|
|
\[ {}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0 \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.306 |
|
|
\[ {}3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.305 |
|
|
\[ {}4 {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x -2 y} y^{\prime }-{\mathrm e}^{2 x -2 y} = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.481 |
|
|
\[ {}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.383 |
|
|
\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.349 |
|
|
\[ {}{y^{\prime }}^{2} x = y \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.632 |
|
|
\[ {}{y^{\prime }}^{2} x +x -2 y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.435 |
|
|
\[ {}{y^{\prime }}^{2} x +y^{\prime } = y \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.362 |
|
|
\[ {}{y^{\prime }}^{2} x +2 y^{\prime }-y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.366 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y^{\prime }-y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.329 |
|
|
\[ {}{y^{\prime }}^{2} x +4 y^{\prime }-2 y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.349 |
|
|
\[ {}{y^{\prime }}^{2} x +x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.375 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }+a = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
0.438 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }+x a = 0 \] |
2 |
2 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.434 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }+a y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.448 |
|
|
\[ {}{y^{\prime }}^{2} x -\left (3 x -y\right ) y^{\prime }+y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.56 |
|
|
\[ {}{y^{\prime }}^{2} x +a +b x -y-b y = 0 \] |
2 |
3 |
1 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.33 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+a = 0 \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.435 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x a = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.293 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.315 |
|
|
\[ {}{y^{\prime }}^{2} x -a y y^{\prime }+b = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
54.294 |
|
|
\[ {}{y^{\prime }}^{2} x +a y y^{\prime }+b x = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.714 |
|
|
\[ {}\left (1+x \right ) {y^{\prime }}^{2} = y \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.651 |
|
|
\[ {}2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.555 |
|
|
\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.287 |
|
|
\[ {}\left (3 x +5\right ) {y^{\prime }}^{2}-\left (3+3 y\right ) y^{\prime }+y = 0 \] |
2 |
3 |
2 |
[_rational, _dAlembert] |
✓ |
✓ |
1.172 |
|
|
\[ {}4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.264 |
|
|
\[ {}4 {y^{\prime }}^{2} x -3 y y^{\prime }+3 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.332 |
|
|
\[ {}4 {y^{\prime }}^{2} x +4 y y^{\prime } = 1 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.421 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+x^{2}-y^{2} = 0 \] |
2 |
4 |
1 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.098 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.512 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+\left (y+2 x \right ) y y^{\prime }+y^{2} = 0 \] |
2 |
3 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.978 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2} = 0 \] |
2 |
3 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.935 |
|
|
\[ {}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+a \left (1-a \right ) x^{2}+y^{2} = 0 \] |
2 |
8 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.332 |
|
|
\[ {}\left (-a^{2}+1\right ) x^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-a^{2} x^{2}+y^{2} = 0 \] |
2 |
8 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
240.952 |
|
|
\[ {}y {y^{\prime }}^{2} = x \,a^{2} \] |
2 |
5 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.892 |
|
|
\[ {}y {y^{\prime }}^{2}+2 a x y^{\prime }-a y = 0 \] |
2 |
5 |
5 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.69 |
|
|
\[ {}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+y a^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.92 |
|
|
\[ {}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
16.224 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (-2 b x +a \right ) y^{\prime }-b y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.815 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
2 |
4 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.855 |
|
|
\[ {}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.695 |
|
|
\[ {}\left (2 x -y\right ) {y^{\prime }}^{2}-2 \left (1-x \right ) y^{\prime }+2-y = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.658 |
|
|
\[ {}2 y {y^{\prime }}^{2}+\left (5-4 x \right ) y^{\prime }+2 y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.544 |
|
|
\[ {}x \left (x -2 y\right ) {y^{\prime }}^{2}-2 x y y^{\prime }-2 x y+y^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.077 |
|
|
\[ {}x \left (x -2 y\right ) {y^{\prime }}^{2}+6 x y y^{\prime }-2 x y+y^{2} = 0 \] |
2 |
9 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
221.604 |
|
|
\[ {}y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+2 y^{2} = 0 \] |
2 |
6 |
6 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.358 |
|
|
\[ {}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0 \] |
2 |
4 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.087 |
|
|
\[ {}\left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0 \] |
2 |
8 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
183.437 |
|
|
\[ {}\left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0 \] |
2 |
4 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.123 |
|
|
\[ {}\left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
11.89 |
|
|
\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.616 |
|
|
\[ {}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0 \] |
2 |
8 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
11.996 |
|
|
\[ {}a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
19.815 |
|
|
\[ {}{y^{\prime }}^{3}+x -y = 0 \] |
3 |
4 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.728 |
|
|
\[ {}{y^{\prime }}^{3}-x y^{\prime }+a y = 0 \] |
3 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
169.119 |
|
|
\[ {}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
3.142 |
|
|
\[ {}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0 \] |
3 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
99.775 |
|
|
\[ {}{y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0 \] |
3 |
2 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.973 |
|
|
\[ {}{y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0 \] |
3 |
4 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
167.053 |
|
|
\[ {}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0 \] |
3 |
4 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
100.448 |
|
|
\[ {}8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \] |
3 |
3 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.527 |
|
|
\[ {}2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0 \] |
3 |
4 |
5 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.613 |
|
|
\[ {}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0 \] |
3 |
6 |
5 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
13.632 |
|
|
\[ {}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \] |
3 |
6 |
5 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
23.288 |
|
|
\[ {}{y^{\prime }}^{3} y-3 x y^{\prime }+3 y = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
173.355 |
|
|
\[ {}2 {y^{\prime }}^{3} y-3 x y^{\prime }+2 y = 0 \] |
3 |
7 |
7 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
154.286 |
|
|
\[ {}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0 \] |
4 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
1.38 |
|
|
\[ {}\left (x -y\right ) \sqrt {y^{\prime }} = a \left (y^{\prime }+1\right ) \] |
2 |
3 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.405 |
|
|
\[ {}a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.764 |
|
|
\[ {}\sqrt {\left (x^{2} a +y^{2}\right ) \left (1+{y^{\prime }}^{2}\right )}-y y^{\prime }-x a = 0 \] |
2 |
8 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
246.119 |
|
|
\[ {}{y^{\prime }}^{2} \left (x +\sin \left (y^{\prime }\right )\right ) = y \] |
0 |
3 |
2 |
[_dAlembert] |
✓ |
✓ |
0.898 |
|
|
\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a +b y = 0 \] |
0 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
3.114 |
|
|
\[ {}\ln \left (y^{\prime }\right )+4 x y^{\prime }-2 y = 0 \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
1.312 |
|
|
\[ {}a \left (\ln \left (y^{\prime }\right )-y^{\prime }\right )-x +y = 0 \] |
0 |
2 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.364 |
|
|
\[ {}y = {y^{\prime }}^{2} x +{y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.309 |
|
|
\[ {}{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1 = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.858 |
|
|
\[ {}y = x y^{\prime }+x \sqrt {1+{y^{\prime }}^{2}} \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
5.283 |
|
|
\[ {}y = x y^{\prime }+a x \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
2 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.856 |
|
|
\[ {}x -y y^{\prime } = a {y^{\prime }}^{2} \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
90.835 |
|
|
\[ {}x +y y^{\prime } = a \sqrt {1+{y^{\prime }}^{2}} \] |
2 |
4 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
38.324 |
|
|
\[ {}y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}} = x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \] |
2 |
3 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
91.131 |
|
|
\[ {}y-2 x y^{\prime } = {y^{\prime }}^{2} x \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.322 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.514 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.341 |
|
|
\[ {}8 y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
5 |
5 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.699 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.482 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.438 |
|
|
\[ {}y = \left (y^{\prime }+1\right ) x +{y^{\prime }}^{2} \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.404 |
|
|
\[ {}y {y^{\prime }}^{2}-x y^{\prime }+3 y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.709 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.368 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.423 |
|
|
\[ {}2 y = {y^{\prime }}^{2}+4 x y^{\prime } \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.429 |
|
|
\[ {}\left (1+{y^{\prime }}^{2}\right ) \left (x -y\right )^{2} = \left (x +y y^{\prime }\right )^{2} \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.073 |
|
|
\[ {}x +y y^{\prime } = a {y^{\prime }}^{2} \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
0.789 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.368 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.498 |
|
|
\[ {}{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y = 0 \] |
3 |
5 |
4 |
[_dAlembert] |
✓ |
✓ |
151.773 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.375 |
|
|
\[ {}{y^{\prime }}^{2}-x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.461 |
|
|
\[ {}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0 \] |
3 |
4 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
94.181 |
|
|
\[ {}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0 \] |
2 |
3 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.528 |
|
|
\[ {}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \] |
3 |
4 |
4 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
6.592 |
|
|
\[ {}4 {y^{\prime }}^{2} x -3 y y^{\prime }+3 = 0 \] |
2 |
2 |
4 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
0.581 |
|
|
\[ {}{y^{\prime }}^{3}-x y^{\prime }+2 y = 0 \] |
3 |
4 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
92.384 |
|
|
\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.694 |
|
|
\[ {}2 {y^{\prime }}^{2} x +\left (2 x -y\right ) y^{\prime }+1-y = 0 \] |
2 |
3 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
1.139 |
|
|
\[ {}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.63 |
|
|
\[ {}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.612 |
|
|
\[ {}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0 \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.564 |
|
|
\[ {}{y^{\prime }}^{4}+x y^{\prime }-3 y = 0 \] |
4 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
3.161 |
|
|
\[ {}{y^{\prime }}^{3}-2 x y^{\prime }-y = 0 \] |
3 |
4 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
101.202 |
|
|
\[ {}y {y^{\prime }}^{2}-\left (x +y\right ) y^{\prime }+y = 0 \] |
2 |
4 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.45 |
|
|
\[ {}y = {y^{\prime }}^{2} x +{y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.378 |
|
|
\[ {}y = {y^{\prime }}^{2} x \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.881 |
|
|
\[ {}y y^{\prime } = 1-x {y^{\prime }}^{3} \] |
3 |
4 |
3 |
[_dAlembert] |
✓ |
✓ |
152.454 |
|
|
\[ {}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x \] |
2 |
3 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.651 |
|
|
\[ {}\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}} = -x \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.527 |
|
|
\[ {}\left (y-2 x y^{\prime }\right )^{2} = {y^{\prime }}^{3} \] |
3 |
8 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
276.817 |
|
|
\[ {}{y^{\prime }}^{2} = x +y \] |
2 |
2 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.018 |
|
|
\[ {}{y^{\prime }}^{2} = \frac {y}{x} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.82 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.687 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.692 |
|
|
\[ {}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
0.981 |
|
|
\[ {}{y^{\prime }}^{2}+a y y^{\prime }-b x -c = 0 \] |
2 |
4 |
1 |
[_dAlembert] |
✓ |
✓ |
91.843 |
|
|
\[ {}3 {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.743 |
|
|
\[ {}a {y^{\prime }}^{2}+y y^{\prime }-x = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
91.692 |
|
|
\[ {}a {y^{\prime }}^{2}-y y^{\prime }-x = 0 \] |
2 |
4 |
2 |
[_dAlembert] |
✓ |
✓ |
1.307 |
|
|
\[ {}{y^{\prime }}^{2} x -y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.808 |
|
|
\[ {}{y^{\prime }}^{2} x +x -2 y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.03 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y^{\prime }-y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.774 |
|
|
\[ {}{y^{\prime }}^{2} x +4 y^{\prime }-2 y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.786 |
|
|
\[ {}{y^{\prime }}^{2} x +x y^{\prime }-y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.789 |
|
|
\[ {}{y^{\prime }}^{2} x +y y^{\prime }+a = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
1.003 |
|
|
\[ {}{y^{\prime }}^{2} x +\left (-3 x +y\right ) y^{\prime }+y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.282 |
|
|
\[ {}{y^{\prime }}^{2} x -y y^{\prime }+a y = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.109 |
|
|
\[ {}{y^{\prime }}^{2} x +2 y y^{\prime }-x = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.729 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+a = 0 \] |
2 |
2 |
3 |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
✓ |
1.007 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.658 |
|
|
\[ {}4 x -2 y y^{\prime }+{y^{\prime }}^{2} x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.582 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.724 |
|
|
\[ {}{y^{\prime }}^{2} x +a y y^{\prime }+b x = 0 \] |
2 |
3 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.891 |
|
|
\[ {}\left (\operatorname {a2} x +\operatorname {c2} \right ) {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {a0} x +\operatorname {b0} y+\operatorname {c0} = 0 \] |
2 |
4 |
2 |
[_rational, _dAlembert] |
✓ |
✓ |
128.933 |
|
|
\[ {}x^{2} {y^{\prime }}^{2}-y \left (-2 x +y\right ) y^{\prime }+y^{2} = 0 \] |
2 |
3 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.429 |
|
|
\[ {}\left (a^{2}-1\right ) x^{2} {y^{\prime }}^{2}+2 x y y^{\prime }-y^{2}+a^{2} x^{2} = 0 \] |
2 |
8 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
213.142 |
|
|
\[ {}a \,x^{2} {y^{\prime }}^{2}-2 a x y y^{\prime }+y^{2}-a \left (a -1\right ) x^{2} = 0 \] |
2 |
8 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.766 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.859 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-9 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.352 |
|
|
\[ {}y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.612 |
|
|
\[ {}y {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.174 |
|
|
\[ {}y {y^{\prime }}^{2}-4 a^{2} x y^{\prime }+y a^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.326 |
|
|
\[ {}y {y^{\prime }}^{2}+a x y^{\prime }+b y = 0 \] |
2 |
4 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
22.196 |
|
|
\[ {}\left (x +y\right ) {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.971 |
|
|
\[ {}\left (-2 x +y\right ) {y^{\prime }}^{2}-2 \left (-1+x \right ) y^{\prime }+y-2 = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.936 |
|
|
\[ {}2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.817 |
|
|
\[ {}4 y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.879 |
|
|
\[ {}a y {y^{\prime }}^{2}+\left (2 x -b \right ) y^{\prime }-y = 0 \] |
2 |
5 |
5 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.192 |
|
|
\[ {}\left (b_{2} y+a_{2} x +c_{2} \right ) {y^{\prime }}^{2}+\left (a_{1} x +b_{1} y+c_{1} \right ) y^{\prime }+a_{0} x +b_{0} y+c_{0} = 0 \] |
2 |
3 |
2 |
[_rational, _dAlembert] |
✓ |
✗ |
9.348 |
|
|
\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+2 x y-y^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.207 |
|
|
\[ {}\left (2 x y-x^{2}\right ) {y^{\prime }}^{2}-6 x y y^{\prime }-y^{2}+2 x y = 0 \] |
2 |
9 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
219.059 |
|
|
\[ {}\left (y^{2}-a^{2} x^{2}\right ) {y^{\prime }}^{2}+2 x y y^{\prime }+\left (-a^{2}+1\right ) x^{2} = 0 \] |
2 |
10 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.904 |
|
|
\[ {}\left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0 \] |
2 |
4 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.012 |
|
|
\[ {}\left (y-x \right )^{2} \left (1+{y^{\prime }}^{2}\right )-a^{2} \left (y^{\prime }+1\right )^{2} = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
18.796 |
|
|
\[ {}3 y^{2} {y^{\prime }}^{2}-2 x y y^{\prime }-x^{2}+4 y^{2} = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.49 |
|
|
\[ {}\left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-2 a^{2} x y y^{\prime }+y^{2}-a^{2} x^{2} = 0 \] |
2 |
7 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
10.343 |
|
|
\[ {}\left (a y-b x \right )^{2} \left (a^{2} {y^{\prime }}^{2}+b^{2}\right )-c^{2} \left (a y^{\prime }+b \right )^{2} = 0 \] |
2 |
6 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
30.862 |
|
|
\[ {}{y^{\prime }}^{3}+a {y^{\prime }}^{2}+b y+a b x = 0 \] |
3 |
4 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
118.026 |
|
|
\[ {}{y^{\prime }}^{3}+{y^{\prime }}^{2} x -y = 0 \] |
3 |
5 |
4 |
[_dAlembert] |
✓ |
✓ |
163.223 |
|
|
\[ {}4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0 \] |
3 |
6 |
5 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
10.048 |
|
|
\[ {}8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \] |
3 |
6 |
5 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
19.878 |
|
|
\[ {}2 {y^{\prime }}^{3} y-y {y^{\prime }}^{2}+2 x y^{\prime }-x = 0 \] |
3 |
4 |
3 |
[_quadrature] |
✓ |
✓ |
0.523 |
|
|
\[ {}{y^{\prime }}^{4}+3 \left (-1+x \right ) {y^{\prime }}^{2}-3 \left (2 y-1\right ) y^{\prime }+3 x = 0 \] |
4 |
3 |
4 |
[_dAlembert] |
✓ |
✓ |
1.138 |
|
|
\[ {}\sqrt {1+{y^{\prime }}^{2}}+{y^{\prime }}^{2} x +y = 0 \] |
4 |
6 |
5 |
[_dAlembert] |
✓ |
✓ |
210.911 |
|
|
\[ {}x \left (\sqrt {1+{y^{\prime }}^{2}}+y^{\prime }\right )-y = 0 \] |
1 |
2 |
2 |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
3.247 |
|
|
\[ {}a x \sqrt {1+{y^{\prime }}^{2}}+x y^{\prime }-y = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.607 |
|
|
\[ {}a \left (1+{y^{\prime }}^{3}\right )^{\frac {1}{3}}+b x y^{\prime }-y = 0 \] |
3 |
4 |
3 |
[_dAlembert] |
✓ |
✓ |
4.359 |
|
|
\[ {}\ln \left (y^{\prime }\right )+x y^{\prime }+a y+b = 0 \] |
0 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.369 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.416 |
|
|
\[ {}2 x y^{\prime }-y+\ln \left (y^{\prime }\right ) = 0 \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
1.593 |
|
|
\[ {}4 {y^{\prime }}^{2} x +2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.349 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.381 |
|
|
\[ {}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.498 |
|
|
\[ {}x +y^{\prime } y \left (2 {y^{\prime }}^{2}+3\right ) = 0 \] |
3 |
7 |
5 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
140.131 |
|
|
\[ {}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.736 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.397 |
|
|
\[ {}4 \,{\mathrm e}^{2 y} {y^{\prime }}^{2}+2 \,{\mathrm e}^{2 x} y^{\prime }-{\mathrm e}^{2 x} = 0 \] |
2 |
2 |
2 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.338 |
|
|
\[ {}\left (x^{2}+y^{2}\right ) \left (y^{\prime }+1\right )^{2}-2 \left (x +y\right ) \left (y^{\prime }+1\right ) \left (x +y y^{\prime }\right )+\left (x +y y^{\prime }\right )^{2} = 0 \] |
2 |
5 |
3 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.897 |
|
|
\[ {}a^{2} y {y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
5 |
4 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.736 |
|
|
\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.42 |
|
|
\[ {}y = \left (1+x \right ) {y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
1.473 |
|
|
\[ {}{y^{\prime }}^{2} x -2 y y^{\prime }-x = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.373 |
|
|
\[ {}8 \left (y^{\prime }+1\right )^{3} = 27 \left (x +y\right ) \left (1-y^{\prime }\right )^{3} \] |
3 |
4 |
4 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
473.104 |
|
|
\[ {}y = 5 x y^{\prime }-{y^{\prime }}^{2} \] |
2 |
3 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.71 |
|
|
\[ {}{y^{\prime }}^{2}-2 x y^{\prime }+y = 0 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.609 |
|
|
\[ {}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0 \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.759 |
|
|
\[ {}y = 2 x y^{\prime }+{y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.43 |
|
|
\[ {}y = {y^{\prime }}^{2} x +{y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.406 |
|
|
\[ {}y = \left (y^{\prime }+1\right ) x +{y^{\prime }}^{2} \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.448 |
|
|
\[ {}y = y {y^{\prime }}^{2}+2 x y^{\prime } \] |
2 |
5 |
7 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.701 |
|
|
\[ {}y = {y^{\prime }}^{2} x +{y^{\prime }}^{2} \] |
2 |
3 |
3 |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.393 |
|
|
\[ {}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \] |
5 |
2 |
1 |
[_dAlembert] |
✓ |
✓ |
0.66 |
|
|
\[ {}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \] |
3 |
5 |
4 |
[_dAlembert] |
✓ |
✓ |
59.272 |
|
|
\[ {}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.661 |
|
|
\[ {}y = 2 x y^{\prime }+\ln \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
2.528 |
|
|
\[ {}y = \left (y^{\prime }+1\right ) x +{y^{\prime }}^{2} \] |
2 |
2 |
1 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.702 |
|
|
\[ {}y = 2 x y^{\prime }+\sin \left (y^{\prime }\right ) \] |
0 |
2 |
2 |
[_dAlembert] |
✓ |
✓ |
1.829 |
|
|
\[ {}y = {y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \] |
3 |
4 |
3 |
[_dAlembert] |
✓ |
✓ |
151.895 |
|
|
\[ {}y = \frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \] |
0 |
2 |
2 |
[_dAlembert] |
✓ |
✓ |
1.561 |
|
|
\[ {}8 {y^{\prime }}^{3}-12 {y^{\prime }}^{2} = 27 y-27 x \] |
3 |
3 |
3 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.437 |
|
|
\[ {}y = {y^{\prime }}^{2}-x y^{\prime }+x \] |
2 |
3 |
3 |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.348 |
|
|
\[ {}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime } \] |
2 |
3 |
6 |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.498 |
|
|
\[ {}3 {y^{\prime }}^{2} x -6 y y^{\prime }+x +2 y = 0 \] |
2 |
3 |
3 |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.298 |
|
|
\[ {}y^{\prime }+{y^{\prime }}^{2} x -y = 0 \] |
2 |
4 |
1 |
[_rational, _dAlembert] |
✓ |
✓ |
0.367 |
|
|
|
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|
|
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|
|