|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime \prime }+2 y^{\prime } y+f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.296 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } y+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0
\] |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.094 |
|
|
\[
{}y^{\prime \prime }+3 y^{\prime } y+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.093 |
|
|
\[
{}y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
0.204 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime } y-3 y^{2} a -4 a^{2} y-b = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
3.114 |
|
|
\[
{}y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
0.204 |
|
|
\[
{}y^{\prime \prime }-2 a y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
43.853 |
|
|
\[
{}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0
\] |
[NONE] |
✗ |
0.099 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.033 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.551 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.527 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.592 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.504 |
|
|
\[
{}y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.262 |
|
|
\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (x \right ) y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.164 |
|
|
\[
{}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.161 |
|
|
\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.171 |
|
|
\[
{}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0
\] |
[NONE] |
✗ |
0.109 |
|
|
\[
{}y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.834 |
|
|
\[
{}y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{v} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.217 |
|
|
\[
{}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.099 |
|
|
\[
{}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0
\] |
[NONE] |
✗ |
0.178 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.496 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.699 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.569 |
|
|
\[
{}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.563 |
|
|
\[
{}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
2.474 |
|
|
\[
{}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
8.461 |
|
|
\[
{}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.294 |
|
|
\[
{}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.136 |
|
|
\[
{}y^{\prime \prime }-f \left (y^{\prime }, a x +b y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.107 |
|
|
\[
{}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.114 |
|
|
\[
{}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{1-n}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.163 |
|
|
\[
{}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.595 |
|
|
\[
{}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.718 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.099 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.099 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.120 |
|
|
\[
{}x y^{\prime \prime }+\left (y-1\right ) y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.576 |
|
|
\[
{}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.158 |
|
|
\[
{}x y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.159 |
|
|
\[
{}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.567 |
|
|
\[
{}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.101 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.107 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.069 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, x y^{\prime }+k y\right ) = 0
\] |
[NONE] |
✗ |
0.141 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left (-y+x y^{\prime }\right )^{2}-b \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.159 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.085 |
|
|
\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.292 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.732 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{4} {y^{\prime }}^{2}+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.085 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+a y^{3}+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.186 |
|
|
\[
{}x^{3} \left (y^{\prime \prime }+y^{\prime } y-y^{3}\right )+12 x y+24 = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.095 |
|
|
\[
{}x^{3} y^{\prime \prime }-a \left (-y+x y^{\prime }\right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.165 |
|
|
\[
{}2 x^{3} y^{\prime \prime }+x^{2} \left (9+2 x y\right ) y^{\prime }+b +x y \left (a +3 x y-2 x^{2} y^{2}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.096 |
|
|
\[
{}2 \left (-x^{k}+4 x^{3}\right ) \left (y^{\prime \prime }+y^{\prime } y-y^{3}\right )-\left (k \,x^{k -1}-12 x^{2}\right ) \left (3 y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
[NONE] |
✗ |
0.127 |
|
|
\[
{}x^{4} y^{\prime \prime }+a^{2} y^{n} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.097 |
|
|
\[
{}x^{4} y^{\prime \prime }-x \left (x^{2}+2 y\right ) y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.156 |
|
|
\[
{}x^{4} y^{\prime \prime }-x^{2} \left (x +y^{\prime }\right ) y^{\prime }+4 y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.157 |
|
|
\[
{}x^{4} y^{\prime \prime }+\left (-y+x y^{\prime }\right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}y^{\prime \prime } \sqrt {x}-y^{{3}/{2}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.117 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{{3}/{2}} y^{\prime \prime }-F \left (\frac {y}{\sqrt {a \,x^{2}+b x +c}}\right ) = 0
\] |
[NONE] |
✗ |
7.986 |
|
|
\[
{}x^{\frac {n}{n +1}} y^{\prime \prime }-y^{\frac {2 n +1}{n +1}} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.149 |
|
|
\[
{}f \left (x \right )^{2} y^{\prime \prime }+f \left (x \right ) f^{\prime }\left (x \right ) y^{\prime }-h \left (y, f \left (x \right ) y^{\prime }\right ) = 0
\] |
[NONE] |
✗ |
0.104 |
|
|
\[
{}y^{\prime \prime } y-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.507 |
|
|
\[
{}y^{\prime \prime } y-a x = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.081 |
|
|
\[
{}y^{\prime \prime } y-a \,x^{2} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.084 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2}-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.701 |
|
|
\[
{}y^{\prime \prime } y+y^{2}-a x -b = 0
\] |
[NONE] |
✗ |
0.088 |
|
|
\[
{}y^{\prime \prime } y+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.574 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.138 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-1 = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.964 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+{\mathrm e}^{x} y \left (c y^{2}+d \right )+{\mathrm e}^{2 x} \left (b +a y^{4}\right ) = 0
\] |
[NONE] |
✗ |
0.128 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.353 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-y^{\prime }+f \left (x \right ) y^{3}+y^{2} \left (\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}\right ) = 0
\] |
[NONE] |
✗ |
0.118 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f \left (x \right ) y^{\prime }-f^{\prime }\left (x \right ) y-y^{3} = 0
\] |
[NONE] |
✗ |
0.105 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+f^{\prime }\left (x \right ) y^{\prime }-f^{\prime \prime }\left (x \right ) y+f \left (x \right ) y^{3}-y^{4} = 0
\] |
[NONE] |
✗ |
0.111 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }+b y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.377 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+a y y^{\prime }-2 y^{2} a +b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.653 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-\left (-1+a y\right ) y^{\prime }+2 a^{2} y^{2}-2 b^{2} y^{3}+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.206 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (-1+a y\right ) y^{\prime }-y \left (y+1\right ) \left (b^{2} y^{2}-a^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
2.255 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (\tan \left (x \right )+\cot \left (x \right )\right ) y y^{\prime }+\left (\cos \left (x \right )^{2}-n^{2} \cot \left (x \right )^{2}\right ) y^{2} \ln \left (y\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
4.269 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-f \left (x \right ) y y^{\prime }-g \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.215 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}+\left (g \left (x \right )+y^{2} f \left (x \right )\right ) y^{\prime }-y \left (g^{\prime }\left (x \right )-f^{\prime }\left (x \right ) y^{2}\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.121 |
|
|
\[
{}y^{\prime \prime } y-3 {y^{\prime }}^{2}+3 y^{\prime } y-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
4.062 |
|
|
\[
{}y^{\prime \prime } y-a {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.362 |
|
|
\[
{}y^{\prime \prime } y+a \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.811 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.427 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y y^{\prime }+c y^{2}+d y^{-a +1} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✗ |
10.363 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.097 |
|
|
\[
{}y^{\prime \prime } y+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
8.234 |
|
|
\[
{}y^{\prime \prime } y-\frac {\left (a -1\right ) {y^{\prime }}^{2}}{a}-f \left (x \right ) y^{2} y^{\prime }+\frac {a f \left (x \right )^{2} y^{4}}{\left (a +2\right )^{2}}-\frac {a f^{\prime }\left (x \right ) y^{3}}{a +2} = 0
\] |
[NONE] |
✗ |
0.137 |
|
|
\[
{}y^{\prime \prime } y-{y^{\prime }}^{2}-1-2 a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
204.332 |
|
|
\[
{}y^{\prime \prime } \left (x +y\right )+{y^{\prime }}^{2}-y^{\prime } = 0
\] |
[[_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]] |
✓ |
4.854 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )+2 y^{\prime } \left (y^{\prime }+1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.145 |
|
|
\[
{}y^{\prime \prime } \left (x -y\right )-\left (y^{\prime }+1\right ) \left (1+{y^{\prime }}^{2}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.152 |
|