|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\] |
[NONE] |
✗ |
0.213 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.075 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{\prime }+f \left (x \right ) y^{3}+y^{2} \left (\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}\right ) = 0
\] |
[NONE] |
✗ |
0.480 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\] |
[NONE] |
✗ |
0.204 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0
\] |
[NONE] |
✗ |
0.464 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.042 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }-2 a y^{2}+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.968 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 b^{2} y^{3}+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
5.071 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (1+y\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
8.825 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
4.360 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.211 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.256 |
|
|
\[
{}y^{\prime \prime } y-3 {y^{\prime }}^{2}+3 y y^{\prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
3.673 |
|
|
\[
{}y^{\prime \prime } y-a {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.351 |
|
|
\[
{}y^{\prime \prime } y+a \left ({y^{\prime }}^{2}+1\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.784 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.250 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{1-a} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✗ |
9.585 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.211 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.899 |
|
|
\[
{}y^{\prime \prime } y-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (a +2\right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{a +2} = 0
\] |
[NONE] |
✗ |
0.271 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-1-2 a y \left ({y^{\prime }}^{2}+1\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
204.953 |
|
|
\[
{}y^{\prime \prime } \left (x +y\right )+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_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]] |
✓ |
4.527 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.140 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left ({y^{\prime }}^{2}+1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.145 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )-h \left (y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.295 |
|
|
\[
{}2 y^{\prime \prime } y+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.987 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.223 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+y^{2} f \left (x \right )+a = 0
\] |
[NONE] |
✗ |
0.189 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.892 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-8 y^{3}-4 y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.275 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-4 \left (x +2 y\right ) y^{2} = 0
\] |
[NONE] |
✗ |
0.141 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (a y+b \right ) y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.611 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+1+2 x y^{2}+a y^{3} = 0
\] |
[NONE] |
✗ |
0.149 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+\left (b x +a y\right ) y^{2} = 0
\] |
[NONE] |
✗ |
0.147 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}-3 y^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.991 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+b -4 \left (x^{2}+a \right ) y^{2}-8 x y^{3}-3 y^{4} = 0
\] |
[[_Painleve, ‘4th‘]] |
✗ |
0.161 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+3 f \left (x \right ) y y^{\prime }+2 \left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y^{2}-8 y^{3} = 0
\] |
[NONE] |
✗ |
0.218 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2}+4 y^{2} y^{\prime }+1+y^{2} f \left (x \right )+y^{4} = 0
\] |
[NONE] |
✗ |
0.207 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.329 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}-4 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.891 |
|
|
\[
{}2 y^{\prime \prime } y-3 {y^{\prime }}^{2}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.179 |
|
|
\[
{}2 y^{\prime \prime } y-6 {y^{\prime }}^{2}+\left (1+a y^{3}\right ) y^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.481 |
|
|
\[
{}2 y^{\prime \prime } y-{y^{\prime }}^{2} \left ({y^{\prime }}^{2}+1\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
68.816 |
|
|
\[
{}2 \left (y-a \right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.118 |
|
|
\[
{}3 y^{\prime \prime } y-2 {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
[NONE] |
✗ |
0.151 |
|
|
\[
{}3 y^{\prime \prime } y-5 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.627 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
14.629 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}-12 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.778 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+a y^{3}+b y^{2}+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
7.464 |
|
|
\[
{}4 y^{\prime \prime } y-3 {y^{\prime }}^{2}+\left (6 y^{2}-\frac {2 f^{\prime }\left (x \right ) y}{f \left (x \right )}\right ) y^{\prime }+y^{4}-2 y^{2} y^{\prime }+g \left (x \right ) y^{2}+f \left (x \right ) y = 0
\] |
[NONE] |
✗ |
0.264 |
|
|
\[
{}4 y^{\prime \prime } y-5 {y^{\prime }}^{2}+a y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.375 |
|
|
\[
{}12 y^{\prime \prime } y-15 {y^{\prime }}^{2}+8 y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.682 |
|
|
\[
{}n y y^{\prime \prime }-\left (n -1\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.358 |
|
|
\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}+\operatorname {c4} y^{4}+\operatorname {c3} y^{3}+\operatorname {c2} y^{2}+\operatorname {c1} y+\operatorname {c0} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.793 |
|
|
\[
{}a y y^{\prime \prime }+b {y^{\prime }}^{2}-\frac {y y^{\prime }}{\sqrt {c^{2}+x^{2}}} = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.797 |
|
|
\[
{}a y y^{\prime \prime }-\left (a -1\right ) {y^{\prime }}^{2}+\left (a +2\right ) f \left (x \right ) y^{2} y^{\prime }+f \left (x \right )^{2} y^{4}+a f^{\prime }\left (x \right ) y^{3} = 0
\] |
[NONE] |
✗ |
0.238 |
|
|
\[
{}\left (a y+b \right ) y^{\prime \prime }+c {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.535 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.735 |
|
|
\[
{}x y y^{\prime \prime }+x {y^{\prime }}^{2}+a y y^{\prime }+f \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.200 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime }+x \left (d +a y^{4}\right )+y \left (c +b y^{2}\right ) = 0
\] |
[[_Painleve, ‘3rd‘]] |
✗ |
0.165 |
|
|
\[
{}x y y^{\prime \prime }-x {y^{\prime }}^{2}+a y y^{\prime }+b x y^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}x y y^{\prime \prime }+2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.628 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+\left (1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.135 |
|
|
\[
{}x y y^{\prime \prime }-2 x {y^{\prime }}^{2}+a y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.228 |
|
|
\[
{}x y y^{\prime \prime }-4 x {y^{\prime }}^{2}+4 y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.537 |
|
|
\[
{}x y y^{\prime \prime }+\left (\frac {a x}{\sqrt {b^{2}-x^{2}}}-x \right ) {y^{\prime }}^{2}-y y^{\prime } = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.324 |
|
|
\[
{}x \left (x +y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }-y = 0
\] |
[[_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]] |
✓ |
0.787 |
|
|
\[
{}2 x y y^{\prime \prime }-x {y^{\prime }}^{2}+y y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.330 |
|
|
\[
{}x^{2} \left (-1+y\right ) y^{\prime \prime }-2 x^{2} {y^{\prime }}^{2}-2 x \left (-1+y\right ) y^{\prime }-2 y \left (-1+y\right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.191 |
|
|
\[
{}x^{2} \left (x +y\right ) y^{\prime \prime }-\left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.161 |
|
|
\[
{}x^{2} \left (x -y\right ) y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.197 |
|
|
\[
{}2 x^{2} y y^{\prime \prime }-x^{2} \left ({y^{\prime }}^{2}+1\right )+y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.154 |
|
|
\[
{}a \,x^{2} y y^{\prime \prime }+b \,x^{2} {y^{\prime }}^{2}+c x y y^{\prime }+d y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.151 |
|
|
\[
{}x \left (x +1\right )^{2} y y^{\prime \prime }-x \left (x +1\right )^{2} {y^{\prime }}^{2}+2 \left (x +1\right )^{2} y y^{\prime }-a \left (x +2\right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.188 |
|
|
\[
{}8 \left (-x^{3}+1\right ) y y^{\prime \prime }-4 \left (-x^{3}+1\right ) {y^{\prime }}^{2}-12 x^{2} y y^{\prime }+3 x y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.173 |
|
|
\[
{}\operatorname {f0} \left (x \right ) y y^{\prime \prime }+\operatorname {f1} \left (x \right ) {y^{\prime }}^{2}+\operatorname {f2} \left (x \right ) y y^{\prime }+\operatorname {f3} \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.256 |
|
|
\[
{}y^{2} y^{\prime \prime }-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
71.474 |
|
|
\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}+a x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.129 |
|
|
\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.141 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+\left (1-2 y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.151 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.373 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.164 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left ({y^{\prime }}^{2}+1\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.151 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left ({y^{\prime }}^{2}+1\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.154 |
|
|
\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+y \left (1-y\right ) y^{\prime } f \left (x \right ) = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.244 |
|
|
\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.369 |
|
|
\[
{}2 y \left (-1+y\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (-1+y\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
0.365 |
|
|
\[
{}-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
[NONE] |
✗ |
0.534 |
|
|
\[
{}3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.520 |
|
|
\[
{}\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.606 |
|
|
\[
{}a y \left (-1+y\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.212 |
|
|
\[
{}a y \left (-1+y\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.860 |
|
|
\[
{}a b y \left (-1+y\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.303 |
|
|
\[
{}x y^{2} y^{\prime \prime }-a = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.130 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.323 |
|
|
\[
{}2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\] |
[[_Painleve, ‘5th‘]] |
✗ |
0.253 |
|
|
\[
{}x^{3} y^{2} y^{\prime \prime }+\left (x +y\right ) \left (-y+y^{\prime } x \right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.166 |
|
|
\[
{}y^{3} y^{\prime \prime }-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.028 |
|
|
\[
{}y \left (1+y^{2}\right ) y^{\prime \prime }+\left (1-3 y^{2}\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.862 |
|
|
\[
{}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\] |
[NONE] |
✗ |
0.145 |
|