|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
2.979 |
|
|
\[
{}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
5.492 |
|
|
\[
{}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.328 |
|
|
\[
{}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
5.862 |
|
|
\[
{}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.014 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.132 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.152 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.145 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.144 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.182 |
|
|
\[
{}x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.454 |
|
|
\[
{}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.130 |
|
|
\[
{}x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.134 |
|
|
\[
{}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.086 |
|
|
\[
{}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.147 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.157 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.135 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.119 |
|
|
\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.239 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.850 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.128 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.148 |
|
|
\[
{}x^{3} \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )+12 x y+24 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.154 |
|
|
\[
{}x^{3} y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.144 |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 y^{2} x^{2}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.164 |
|
|
\[
{}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y y^{\prime }-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+y a x +b = 0
\] |
[NONE] |
✗ |
0.352 |
|
|
\[
{}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.131 |
|
|
\[
{}x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.128 |
|
|
\[
{}x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.132 |
|
|
\[
{}x^{4} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.125 |
|
|
\[
{}y^{\prime \prime } \sqrt {x}-y^{{3}/{2}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.154 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right ) = 0
\] |
[NONE] |
✗ |
8.835 |
|
|
\[
{}y^{\prime \prime } y-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.820 |
|
|
\[
{}y^{\prime \prime } y-a x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.112 |
|
|
\[
{}y^{\prime \prime } y-a \,x^{2} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.115 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2}-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.016 |
|
|
\[
{}y^{\prime \prime } y+y^{2}-a x -b = 0
\] |
[NONE] |
✗ |
0.125 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.875 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.173 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.309 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\] |
[NONE] |
✗ |
0.289 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.118 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\] |
[NONE] |
✗ |
0.217 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0
\] |
[NONE] |
✗ |
0.313 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.621 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
3.319 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 b^{2} y^{3}+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
6.093 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
10.332 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
4.381 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.222 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.372 |
|
|
\[
{}y^{\prime \prime } y-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.953 |
|
|
\[
{}y^{\prime \prime } y-a {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.344 |
|
|
\[
{}y^{\prime \prime } y+a \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.703 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.175 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✗ |
10.645 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.474 |
|
|
\[
{}y^{\prime \prime } y-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (a +2\right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{a +2} = 0
\] |
[NONE] |
✗ |
0.382 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
48.854 |
|
|
\[
{}y^{\prime \prime } \left (x +y\right )+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.250 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.123 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.126 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.406 |
|
|
\[
{}2 y^{\prime \prime } y+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.905 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.062 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0
\] |
[NONE] |
✗ |
0.204 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
74.992 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
66.453 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2} = 0
\] |
[NONE] |
✗ |
0.140 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
16.109 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\] |
[NONE] |
✗ |
0.144 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\] |
[NONE] |
✗ |
0.139 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-3 y^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.333 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\] |
[[_Painleve, ‘4th‘]] |
✗ |
0.163 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.349 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}-4 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.629 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.193 |
|
|
\[
{}2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.154 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2} \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.516 |
|
|
\[
{}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.519 |
|
|
\[
{}3 y^{\prime \prime } y-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
[NONE] |
✗ |
0.132 |
|
|
\[
{}3 y^{\prime \prime } y-5 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.430 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.087 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}-12 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
24.495 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.702 |
|
|
\[
{}4 y^{\prime \prime } y-5 {y^{\prime }}^{2}+a y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.518 |
|
|
\[
{}12 y^{\prime \prime } y-15 {y^{\prime }}^{2}+8 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.218 |
|
|
\[
{}n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.397 |
|
|
\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.088 |
|
|
\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.417 |
|
|
\[
{}\left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.373 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.118 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.192 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\] |
[[_Painleve, ‘3rd‘]] |
✗ |
0.168 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.145 |
|
|
\[
{}x y y^{\prime \prime }+2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.759 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (y+1\right ) y^{\prime } = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.121 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.214 |
|
|
\[
{}x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.546 |
|