|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right ) = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
2.669 |
|
|
\[
{}y^{\left (5\right )}-a x y-b = 0
\] |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
0.040 |
|
|
\[
{}y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.049 |
|
|
\[
{}y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.109 |
|
|
\[
{}x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.040 |
|
|
\[
{}x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.340 |
|
|
\[
{}x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime } = 0
\] |
[[_high_order, _missing_y]] |
✗ |
0.069 |
|
|
\[
{}x^{2} y^{\prime \prime \prime \prime }-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.044 |
|
|
\[
{}x^{10} y^{\left (5\right )}-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.045 |
|
|
\[
{}x^{{5}/{2}} y^{\left (5\right )}-a y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.058 |
|
|
\[
{}\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✗ |
0.055 |
|
|
\[
{}y^{\prime \prime }-y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.737 |
|
|
\[
{}y^{\prime \prime }-6 y^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.667 |
|
|
\[
{}y^{\prime \prime }-6 y^{2}-x = 0
\] |
[[_Painleve, ‘1st‘]] |
✗ |
0.076 |
|
|
\[
{}y^{\prime \prime }-6 y^{2}+4 y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.593 |
|
|
\[
{}y^{\prime \prime }+a y^{2}+b x +c = 0
\] |
[NONE] |
✗ |
0.081 |
|
|
\[
{}y^{\prime \prime }-2 y^{3}-y x +a = 0
\] |
[[_Painleve, ‘2nd‘]] |
✗ |
0.084 |
|
|
\[
{}y^{\prime \prime }-a y^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.494 |
|
|
\[
{}y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b = 0
\] |
[NONE] |
✗ |
0.087 |
|
|
\[
{}y^{\prime \prime }+d +b x y+c y+a y^{3} = 0
\] |
[NONE] |
✗ |
0.087 |
|
|
\[
{}y^{\prime \prime }+d +b y^{2}+c y+a y^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
3.878 |
|
|
\[
{}y^{\prime \prime }+a \,x^{r} y^{2} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.089 |
|
|
\[
{}y^{\prime \prime }+6 a^{10} y^{11}-y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.894 |
|
|
\[
{}y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}} = 0
\] |
[NONE] |
✗ |
0.193 |
|
|
\[
{}y^{\prime \prime }-{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
34.526 |
|
|
\[
{}y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.115 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.161 |
|
|
\[
{}y^{\prime \prime }+a \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.052 |
|
|
\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.284 |
|
|
\[
{}y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.189 |
|
|
\[
{}y^{\prime \prime } = \frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.237 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.481 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.074 |
|
|
\[
{}y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.549 |
|
|
\[
{}y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.546 |
|
|
\[
{}y^{\prime \prime }-\frac {\left (3 n +4\right ) y^{\prime }}{n}-\frac {2 \left (n +1\right ) \left (n +2\right ) y \left (y^{\frac {n}{n +1}}-1\right )}{n^{2}} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.331 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b y^{n}+\frac {\left (a^{2}-1\right ) y}{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.990 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n} = 0
\] |
[NONE] |
✗ |
0.093 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.757 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.128 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime }-y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
20.342 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime }-y^{3}+a y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.974 |
|
|
\[
{}y^{\prime \prime }+\left (y+3 a \right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.113 |
|
|
\[
{}y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+y^{2} f \left (x \right )+y \left (f^{\prime }\left (x \right )+2 f \left (x \right )^{2}\right ) = 0
\] |
[NONE] |
✗ |
0.101 |
|
|
\[
{}y^{\prime \prime }+y y^{\prime }-y^{3}-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+f \left (x \right )\right ) \left (3 y^{\prime }+y^{2}\right )+\left (a f \left (x \right )^{2}+3 f^{\prime }\left (x \right )+\frac {3 {f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}\right ) y+b f \left (x \right )^{3} = 0
\] |
[NONE] |
✗ |
0.122 |
|
|
\[
{}y^{\prime \prime }+\left (y-\frac {3 f^{\prime }\left (x \right )}{2 f \left (x \right )}\right ) y^{\prime }-y^{3}-\frac {f^{\prime }\left (x \right ) y^{2}}{2 f \left (x \right )}+\frac {\left (f \left (x \right )+\frac {{f^{\prime }\left (x \right )}^{2}}{f \left (x \right )^{2}}-f^{\prime \prime }\left (x \right )\right ) y}{2 f \left (x \right )} = 0
\] |
[NONE] |
✗ |
0.124 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) y^{\prime }+f^{\prime }\left (x \right ) y = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
1.214 |
|
|
\[
{}y^{\prime \prime }+2 y y^{\prime }+f \left (x \right ) \left (y^{\prime }+y^{2}\right )-g \left (x \right ) = 0
\] |
[[_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.086 |
|
|
\[
{}y^{\prime \prime }+3 y y^{\prime }+y^{3}+f \left (x \right ) y-g \left (x \right ) = 0
\] |
[NONE] |
✗ |
0.088 |
|
|
\[
{}y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
0.086 |
|
|
\[
{}y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.849 |
|
|
\[
{}y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+y^{2} f \left (x \right ) = 0
\] |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
0.091 |
|
|
\[
{}y^{\prime \prime }-2 a y y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.619 |
|
|
\[
{}y^{\prime \prime }+a y y^{\prime }+b y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
43.576 |
|
|
\[
{}y^{\prime \prime }+f \left (x , y\right ) y^{\prime }+g \left (x , y\right ) = 0
\] |
[NONE] |
✗ |
0.084 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.968 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.519 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{\prime }+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.444 |
|
|
\[
{}y^{\prime \prime }+a {y^{\prime }}^{2}+b \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
4.569 |
|
|
\[
{}y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.472 |
|
|
\[
{}y^{\prime \prime }+a y {y^{\prime }}^{2}+b y = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.189 |
|
|
\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (x \right ) y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.428 |
|
|
\[
{}y^{\prime \prime }-\frac {D\left (f \right )\left (y\right ) {y^{\prime }}^{3}}{f \left (y\right )}+g \left (x \right ) y^{\prime }+h \left (x \right ) f \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.151 |
|
|
\[
{}y^{\prime \prime }+\phi \left (y\right ) {y^{\prime }}^{2}+f \left (x \right ) y^{\prime }+g \left (x \right ) \Phi \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.149 |
|
|
\[
{}y^{\prime \prime }+f \left (y\right ) {y^{\prime }}^{2}+g \left (y\right ) y^{\prime }+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.161 |
|
|
\[
{}y^{\prime \prime }+\left (1+{y^{\prime }}^{2}\right ) \left (f \left (x , y\right ) y^{\prime }+g \left (x , y\right )\right ) = 0
\] |
[NONE] |
✗ |
0.102 |
|
|
\[
{}y^{\prime \prime }+a y \left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.664 |
|
|
\[
{}y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.096 |
|
|
\[
{}y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}y^{\prime \prime }+\left (y^{\prime }-\frac {y}{x}\right )^{a} f \left (x , y\right ) = 0
\] |
[NONE] |
✗ |
0.168 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.465 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {1+{y^{\prime }}^{2}}+b
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.638 |
|
|
\[
{}y^{\prime \prime } = a \sqrt {{y^{\prime }}^{2}+b y^{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.047 |
|
|
\[
{}y^{\prime \prime } = a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.501 |
|
|
\[
{}y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
2.424 |
|
|
\[
{}y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
8.149 |
|
|
\[
{}y^{\prime \prime } = 2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.158 |
|
|
\[
{}y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
3.998 |
|
|
\[
{}y^{\prime \prime }-f \left (y^{\prime }, a x +b y\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.098 |
|
|
\[
{}y^{\prime \prime }-y f \left (x , \frac {y^{\prime }}{y}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.099 |
|
|
\[
{}y^{\prime \prime }-x^{n -2} f \left (y x^{-n}, y^{\prime } x^{-n +1}\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.151 |
|
|
\[
{}8 y^{\prime \prime }+9 {y^{\prime }}^{4} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.545 |
|
|
\[
{}a y^{\prime \prime }+h \left (y^{\prime }\right )+c y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.713 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y^{n} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.088 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{v} y^{n} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.096 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.082 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x \,{\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.084 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.112 |
|
|
\[
{}x y^{\prime \prime }+\left (-1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.518 |
|
|
\[
{}x y^{\prime \prime }-x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.082 |
|
|
\[
{}x y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.082 |
|
|
\[
{}2 x y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.526 |
|
|
\[
{}x^{2} y^{\prime \prime } = a \left (y^{n}-y\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.097 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.473 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a +1\right ) x y^{\prime }-x^{k} f \left (x^{k} y, y^{\prime } x +k y\right ) = 0
\] |
[NONE] |
✗ |
0.127 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b \,x^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.087 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y {y^{\prime }}^{2}+b x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.077 |
|
|
\[
{}x^{2} y^{\prime \prime }-\sqrt {a \,x^{2} {y^{\prime }}^{2}+b y^{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.152 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+{y^{\prime }}^{2}+1 = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.695 |
|