|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{2} y^{\prime \prime }+y {y^{\prime }}^{2}-a x -b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.076 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+\left (1-2 y\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
2.252 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }-3 y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.343 |
|
|
\[
{}\left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.095 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.089 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime \prime }-2 \left (1+{y^{\prime }}^{2}\right ) \left (-y+y^{\prime } x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
0.090 |
|
|
\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-2 y\right ) {y^{\prime }}^{2}+y \left (1-y\right ) y^{\prime } f \left (x \right ) = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.101 |
|
|
\[
{}2 y \left (1-y\right ) y^{\prime \prime }-\left (1-3 y\right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.135 |
|
|
\[
{}2 y \left (-1+y\right ) y^{\prime \prime }-\left (3 y-1\right ) {y^{\prime }}^{2}+4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+4 y^{2} \left (-1+y\right ) \left (g \left (x \right )^{2}-f \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
0.132 |
|
|
\[
{}-2 y \left (1-y\right ) y^{\prime \prime }+\left (1-3 y\right ) {y^{\prime }}^{2}-4 y y^{\prime } \left (f \left (x \right ) y+g \left (x \right )\right )+\left (1-y\right )^{3} \left (\operatorname {f0} \left (x \right )^{2} y^{2}-\operatorname {f1} \left (x \right )^{2}\right )+4 y^{2} \left (1-y\right ) \left (f \left (x \right )^{2}-g \left (x \right )^{2}-g^{\prime }\left (x \right )-f^{\prime }\left (x \right )\right ) = 0
\] |
[NONE] |
✗ |
0.149 |
|
|
\[
{}3 y \left (1-y\right ) y^{\prime \prime }-2 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.137 |
|
|
\[
{}\left (1-y\right ) y^{\prime \prime }-3 \left (1-2 y\right ) {y^{\prime }}^{2}-h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.135 |
|
|
\[
{}a y \left (-1+y\right ) y^{\prime \prime }+\left (b y+c \right ) {y^{\prime }}^{2}+h \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.137 |
|
|
\[
{}a y \left (-1+y\right ) y^{\prime \prime }-\left (a -1\right ) \left (2 y-1\right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.795 |
|
|
\[
{}a b y \left (-1+y\right ) y^{\prime \prime }-\left (\left (2 a b -a -b \right ) y+\left (1-a \right ) b \right ) {y^{\prime }}^{2}+f y \left (-1+y\right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.277 |
|
|
\[
{}x y^{2} y^{\prime \prime }-a = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
0.078 |
|
|
\[
{}\left (a^{2}-x^{2}\right ) \left (a^{2}-y^{2}\right ) y^{\prime \prime }+\left (a^{2}-x^{2}\right ) y {y^{\prime }}^{2}-x \left (a^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
0.106 |
|
|
\[
{}2 x^{2} y \left (-1+y\right ) y^{\prime \prime }-x^{2} \left (3 y-1\right ) {y^{\prime }}^{2}+2 x y \left (-1+y\right ) y^{\prime }+\left (a y^{2}+b \right ) \left (-1+y\right )^{3}+c x y^{2} \left (-1+y\right )+d \,x^{2} y^{2} \left (1+y\right ) = 0
\] |
[[_Painleve, ‘5th‘]] |
✗ |
0.111 |
|
|
\[
{}x^{3} y^{2} y^{\prime \prime }+\left (x +y\right ) \left (-y+y^{\prime } x \right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.091 |
|
|
\[
{}y^{3} y^{\prime \prime }-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
1.022 |
|
|
\[
{}y \left (1+y^{2}\right ) y^{\prime \prime }+\left (1-3 y^{2}\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.887 |
|
|
\[
{}2 y^{3} y^{\prime \prime }+y^{4}-a^{2} x y^{2}-1 = 0
\] |
[NONE] |
✗ |
0.083 |
|
|
\[
{}2 y^{3} y^{\prime \prime }+y^{2} {y^{\prime }}^{2}-a \,x^{2}-b x -c = 0
\] |
[NONE] |
✗ |
0.081 |
|
|
\[
{}2 \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) y^{\prime \prime }-\left (\left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right )+\left (y-b \right ) \left (y-c \right )\right ) {y^{\prime }}^{2}+\left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} \left (A_{0} +\frac {B_{0}}{\left (y-a \right )^{2}}+\frac {C_{1}}{\left (y-b \right )^{2}}+\frac {D_{0}}{\left (y-c \right )^{2}}\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
42.226 |
|
|
\[
{}\left (4 y^{3}-a y-b \right ) y^{\prime \prime }-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.881 |
|
|
\[
{}\left (4 y^{3}-a y-b \right ) \left (y^{\prime \prime }+f y^{\prime }\right )-\left (6 y^{2}-\frac {a}{2}\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.295 |
|
|
\[
{}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }+x \left (1-x \right ) \left (x -2 y x -2 y+3 y^{2}\right ) {y^{\prime }}^{2}+2 y \left (1-y\right ) \left (x^{2}+y-2 y x \right ) y^{\prime }-y^{2} \left (1-y\right )^{2}-f \left (y \left (-1+y\right ) \left (-x +y\right )\right )^{{3}/{2}} = 0
\] |
unknown |
✗ |
0.220 |
|
|
\[
{}2 x^{2} y \left (1-x \right )^{2} \left (1-y\right ) \left (x -y\right ) y^{\prime \prime }-x^{2} \left (1-x \right )^{2} \left (x -2 y x -2 y+3 y^{2}\right ) {y^{\prime }}^{2}-2 x y \left (1-x \right ) \left (1-y\right ) \left (x^{2}+y-2 y x \right ) y^{\prime }+b x \left (1-y\right )^{2} \left (x -y\right )^{2}-c \left (1-x \right ) y^{2} \left (x -y\right )^{2}-d x y^{2} \left (1-x \right ) \left (1-y\right )^{2}+a y^{2} \left (x -y\right )^{2} \left (1-y\right )^{2} = 0
\] |
[[_Painleve, ‘6th‘]] |
✗ |
0.148 |
|
|
\[
{}\left (-1+y^{2}\right ) \left (a^{2} y^{2}-1\right ) y^{\prime \prime }+b \sqrt {\left (1-y^{2}\right ) \left (1-a^{2} y^{2}\right )}\, {y^{\prime }}^{2}+\left (1+a^{2}-2 a^{2} y^{2}\right ) y {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
9.381 |
|
|
\[
{}\left (c +2 b x +a \,x^{2}+y^{2}\right )^{2} y^{\prime \prime }+d y = 0
\] |
[NONE] |
✗ |
0.094 |
|
|
\[
{}\sqrt {y}\, y^{\prime \prime }-a = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
0.671 |
|
|
\[
{}\sqrt {x^{2}+y^{2}}\, y^{\prime \prime }-a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.194 |
|
|
\[
{}y \left (1-\ln \left (y\right )\right ) y^{\prime \prime }+\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.444 |
|
|
\[
{}\left (b +a \sin \left (y\right )^{2}\right ) y^{\prime \prime }+a {y^{\prime }}^{2} \cos \left (y\right ) \sin \left (y\right )+A y \left (c +a \sin \left (y\right )^{2}\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
76.676 |
|
|
\[
{}h \left (y\right ) y^{\prime \prime }+a h \left (y\right ) {y^{\prime }}^{2}+j \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
0.129 |
|
|
\[
{}h \left (y\right ) y^{\prime \prime }-D\left (h \right )\left (y\right ) {y^{\prime }}^{2}-h \left (y\right )^{2} j \left (x , \frac {y^{\prime }}{h \left (y\right )}\right ) = 0
\] |
[NONE] |
✗ |
0.138 |
|
|
\[
{}y^{\prime } y^{\prime \prime }-x^{2} y y^{\prime }-x y^{2} = 0
\] |
[[_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_poly_yn]] |
✗ |
2.776 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.082 |
|
|
\[
{}\left (-y+y^{\prime } x \right ) y^{\prime \prime }-\left (1+{y^{\prime }}^{2}\right )^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.085 |
|
|
\[
{}a \,x^{3} y^{\prime } y^{\prime \prime }+b y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.081 |
|
|
\[
{}\left (\operatorname {f1} y^{\prime }+\operatorname {f2} y\right ) y^{\prime \prime }+\operatorname {f3} {y^{\prime }}^{2}+\operatorname {f4} \left (x \right ) y y^{\prime }+\operatorname {f5} \left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.092 |
|
|
\[
{}\left (2 y^{2} y^{\prime }+x^{2}\right ) y^{\prime \prime }+2 y {y^{\prime }}^{3}+3 y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_poly_yn]] |
✗ |
7.977 |
|
|
\[
{}\left ({y^{\prime }}^{2}+y^{2}\right ) y^{\prime \prime }+y^{3} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
38.482 |
|
|
\[
{}\left ({y^{\prime }}^{2}+a \left (-y+y^{\prime } x \right )\right ) y^{\prime \prime }-b = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.081 |
|
|
\[
{}\left (a \sqrt {1+{y^{\prime }}^{2}}-y^{\prime } x \right ) y^{\prime \prime }-{y^{\prime }}^{2}-1 = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
691.523 |
|
|
\[
{}h \left (y^{\prime }\right ) y^{\prime \prime }+j \left (y\right ) y^{\prime }+f = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
0.153 |
|
|
\[
{}{y^{\prime \prime }}^{2}-a y-b = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
0.092 |
|
|
\[
{}a^{2} {y^{\prime \prime }}^{2}-2 a x y^{\prime \prime }+y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
5.066 |
|
|
\[
{}2 \left (x^{2}+1\right ) {y^{\prime \prime }}^{2}-x y^{\prime \prime } \left (x +4 y^{\prime }\right )+2 \left (x +y^{\prime }\right ) y^{\prime }-2 y = 0
\] |
[NONE] |
✗ |
0.085 |
|
|
\[
{}3 x^{2} {y^{\prime \prime }}^{2}-2 \left (3 y^{\prime } x +y\right ) y^{\prime \prime }+4 {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.101 |
|
|
\[
{}x^{2} \left (2-9 x \right ) {y^{\prime \prime }}^{2}-6 x \left (1-6 x \right ) y^{\prime } y^{\prime \prime }+6 y^{\prime \prime } y-36 x {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.115 |
|
|
\[
{}F_{1,1}\left (x \right ) {y^{\prime }}^{2}+\left (\left (F_{2,1}\left (x \right )+F_{1,2}\left (x \right )\right ) y^{\prime \prime }+y \left (F_{1,0}\left (x \right )+F_{0,1}\left (x \right )\right )\right ) y^{\prime }+F_{2,2}\left (x \right ) {y^{\prime \prime }}^{2}+y \left (F_{2,0}\left (x \right )+F_{0,2}\left (x \right )\right ) y^{\prime \prime }+F_{0,0}\left (x \right ) y^{2} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.095 |
|
|
\[
{}y {y^{\prime \prime }}^{2}-a \,{\mathrm e}^{2 x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.136 |
|
|
\[
{}\left (a^{2} y^{2}-b^{2}\right ) {y^{\prime \prime }}^{2}-2 a^{2} y {y^{\prime }}^{2} y^{\prime \prime }+\left (a^{2} {y^{\prime }}^{2}-1\right ) {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
14.414 |
|
|
\[
{}\left (y^{2}-x^{2} {y^{\prime }}^{2}+x^{2} y y^{\prime \prime }\right )^{2}-4 x y \left (-y+y^{\prime } x \right )^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.095 |
|
|
\[
{}\left (2 y^{\prime \prime } y-{y^{\prime }}^{2}\right )^{3}+32 y^{\prime \prime } \left (x y^{\prime \prime }-y^{\prime }\right )^{3} = 0
\] |
unknown |
✗ |
0.451 |
|
|
\[
{}\sqrt {a {y^{\prime \prime }}^{2}+b {y^{\prime }}^{2}}+c y y^{\prime \prime }+d {y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
10.457 |
|
|
\[
{}y^{\prime \prime \prime }-a^{2} \left ({y^{\prime }}^{5}+2 {y^{\prime }}^{3}+y^{\prime }\right ) = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
3.271 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime } y-{y^{\prime }}^{2}+1 = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}y^{\prime \prime \prime }-y^{\prime \prime } y+{y^{\prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.044 |
|
|
\[
{}y^{\prime \prime \prime }+a y y^{\prime \prime } = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.042 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+x y^{\prime \prime }+\left (2 y x -1\right ) y^{\prime }+y^{2}-f \left (x \right ) = 0
\] |
[[_3rd_order, _exact, _nonlinear]] |
✗ |
0.044 |
|
|
\[
{}x^{2} y^{\prime \prime \prime }+x \left (-1+y\right ) y^{\prime \prime }+x {y^{\prime }}^{2}+\left (1-y\right ) y^{\prime } = 0
\] |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✗ |
0.055 |
|
|
\[
{}y y^{\prime \prime \prime }-y^{\prime } y^{\prime \prime }+y^{3} y^{\prime } = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.045 |
|
|
\[
{}4 y^{2} y^{\prime \prime \prime }-18 y y^{\prime } y^{\prime \prime }+15 {y^{\prime }}^{3} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.046 |
|
|
\[
{}9 y^{2} y^{\prime \prime \prime }-45 y y^{\prime } y^{\prime \prime }+40 {y^{\prime }}^{3} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.047 |
|
|
\[
{}2 y^{\prime } y^{\prime \prime \prime }-3 {y^{\prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.526 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-3 y^{\prime } {y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
0.341 |
|
|
\[
{}\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }-\left (3 y^{\prime }+a \right ) {y^{\prime \prime }}^{2} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
6.941 |
|
|
\[
{}y^{\prime \prime } y^{\prime \prime \prime }-a \sqrt {b^{2} {y^{\prime \prime }}^{2}+1} = 0
\] |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
8.312 |
|
|
\[
{}y^{\prime } y^{\prime \prime \prime \prime }-y^{\prime \prime } y^{\prime \prime \prime }+{y^{\prime }}^{3} y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
0.072 |
|
|
\[
{}y^{\prime } \left (f^{\prime \prime \prime }\left (x \right ) y^{\prime }+3 f^{\prime \prime }\left (x \right ) y^{\prime \prime }+3 f^{\prime }\left (x \right ) y^{\prime \prime \prime }+f \left (x \right ) y^{\prime \prime \prime \prime }\right )-y^{\prime \prime } f y^{\prime \prime \prime }+{y^{\prime }}^{3} \left (f^{\prime }\left (x \right ) y^{\prime }+f \left (x \right ) y^{\prime \prime }\right )+2 q \left (x \right ) {y^{\prime }}^{2} \sin \left (y\right )+\left (q \left (x \right ) y^{\prime \prime }-q^{\prime }\left (x \right ) y^{\prime }\right ) \cos \left (y\right ) = 0
\] |
[NONE] |
✗ |
0.063 |
|
|
\[
{}3 y^{\prime \prime } y^{\prime \prime \prime \prime }-5 {y^{\prime \prime \prime }}^{2} = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
0.623 |
|
|
\[
{}9 {y^{\prime \prime }}^{2} y^{\left (5\right )}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+40 y^{\prime \prime \prime } = 0
\] |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
0.077 |
|
|
\[
{}y^{\prime \prime }-f \left (y\right ) = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✗ |
0.128 |
|
|
\[
{}y^{\prime \prime \prime } = f \left (y\right )
\] |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
0.014 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x \\ y^{\prime }=b \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a y \\ y^{\prime }=-a x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.306 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a y \\ y^{\prime }=b x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.355 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x-y \\ y^{\prime }=x+a y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.312 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+b y \\ y^{\prime }=c x+b y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.671 |
|
|
\[
{}\left [\begin {array}{c} a x^{\prime }+b y^{\prime }=\alpha x+\beta y \\ b x^{\prime }-a y^{\prime }=\beta x-\alpha y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.665 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.381 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x+4 y=0 \\ y^{\prime }+2 x+5 y=0 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.296 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.372 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a_{1} x+b_{1} y+c_{1} \\ y^{\prime }=a_{2} x+b_{2} y+c_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.425 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 y=3 t \\ y^{\prime }-2 x=4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y-t^{2}+6 t +1=0 \\ y^{\prime }-x=-3 t^{2}+3 t +1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.607 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+3 x-y={\mathrm e}^{2 t} \\ y^{\prime }+x+5 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.484 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+2 x+y^{\prime }+y={\mathrm e}^{2 t}+t \\ x^{\prime }-x+y^{\prime }+3 y={\mathrm e}^{t}-1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.197 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+y^{\prime }-y={\mathrm e}^{t} \\ 2 x^{\prime }+y^{\prime }+2 y=\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.532 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+2 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+x+24 y=3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.712 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+11 x+31 y={\mathrm e}^{t} \\ 3 x^{\prime }+7 y^{\prime }+8 x+24 y={\mathrm e}^{2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} 4 x^{\prime }+9 y^{\prime }+44 x+49 y=t \\ 3 x^{\prime }+7 y^{\prime }+34 x+38 y={\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x f \left (t \right )+y g \left (t \right ) \\ y^{\prime }=-x g \left (t \right )+y f \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }+\left (a x+b y\right ) f \left (t \right )=g \left (t \right ) \\ y^{\prime }+\left (c x+d y\right ) f \left (t \right )=h \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \cos \left (t \right ) \\ y^{\prime }=x \,{\mathrm e}^{-\sin \left (t \right )} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.057 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+y=0 \\ t y^{\prime }+x=0 \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.046 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x=t \\ t y^{\prime }-\left (t +2\right ) x-t y=-t \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.083 |
|
|
\[
{}\left [\begin {array}{c} t x^{\prime }+2 x-2 y=t \\ t y^{\prime }+x+5 y=t^{2} \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|