|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.416 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.430 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.417 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.373 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.836 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-12 y-14 z \\ y^{\prime }=x+2 y-3 z \\ z^{\prime }=x+y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.636 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.515 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
2.688 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
2.030 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
3.199 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0
\] |
[_separable] |
✓ |
2.664 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
1.525 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_quadrature] |
✓ |
1.544 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (x y+1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
1.237 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} x^{2} = 0
\] |
[_separable] |
✓ |
2.450 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.920 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
3.782 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
2.567 |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[_quadrature] |
✓ |
3.862 |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.927 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (-1+x y^{2}\right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
2.228 |
|
|
\[
{}\left (y^{2}+x^{2}\right )^{2} {y^{\prime }}^{2} = 4 y^{2} x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.564 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+\left (y-x \right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.825 |
|
|
\[
{}x y \left (y^{2}+x^{2}\right ) \left (-1+{y^{\prime }}^{2}\right ) = y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.868 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
1.766 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
1.555 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.623 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.976 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.457 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.355 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.412 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.478 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.291 |
|
|
\[
{}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\] |
[_dAlembert] |
✓ |
2.937 |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
108.488 |
|
|
\[
{}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.531 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.377 |
|
|
\[
{}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
117.715 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.346 |
|
|
\[
{}y = x y^{\prime }+k {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.377 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.368 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.167 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.609 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.023 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.547 |
|
|
\[
{}y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.511 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
9.785 |
|
|
\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
11.859 |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.962 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.636 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.467 |
|
|
\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.536 |
|
|
\[
{}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.551 |
|
|
\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.555 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.514 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.531 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.477 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.149 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.484 |
|
|
\[
{}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.483 |
|
|
\[
{}y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.012 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.727 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.603 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.602 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.398 |
|
|
\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.351 |
|
|
\[
{}\left (1+y\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.257 |
|
|
\[
{}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.405 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.526 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.590 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.274 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.613 |
|
|
\[
{}y^{\prime \prime }+\beta ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.648 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.526 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime } = y^{\prime }
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.900 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.359 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.306 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
21.572 |
|
|
\[
{}y^{\prime \prime } = -{\mathrm e}^{-2 y}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
24.141 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.805 |
|
|
\[
{}2 y^{\prime \prime } = \sin \left (2 y\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.870 |
|
|
\[
{}x^{3} y^{\prime \prime }-x^{2} y^{\prime } = -x^{2}+3
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.981 |
|
|
\[
{}y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.188 |
|
|
\[
{}y^{\prime \prime } = {\mathrm e}^{x} {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.230 |
|
|
\[
{}2 y^{\prime \prime } = {y^{\prime }}^{3} \sin \left (2 x \right )
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.038 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.244 |
|
|
\[
{}y^{\prime \prime } = 1+{y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.380 |
|
|
\[
{}y^{\prime \prime } = \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.504 |
|
|
\[
{}y y^{\prime \prime } = {y^{\prime }}^{2} \left (1-y^{\prime } \sin \left (y\right )-y y^{\prime } \cos \left (y\right )\right )
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
1.142 |
|
|
\[
{}\left (1+y^{2}\right ) y^{\prime \prime }+{y^{\prime }}^{3}+y^{\prime } = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
2.089 |
|
|
\[
{}\left (y y^{\prime \prime }+1+{y^{\prime }}^{2}\right )^{2} = \left (1+{y^{\prime }}^{2}\right )^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
13.167 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (2 x -y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.676 |
|
|
\[
{}x^{2} y^{\prime \prime } = y^{\prime } \left (3 x -2 y^{\prime }\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.444 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime } \left (2-3 x y^{\prime }\right )
\] |
[[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.520 |
|
|
\[
{}x^{4} y^{\prime \prime } = y^{\prime } \left (y^{\prime }+x^{3}\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.775 |
|
|
\[
{}y^{\prime \prime } = 2 x +\left (x^{2}-y^{\prime }\right )^{2}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.664 |
|
|
\[
{}{y^{\prime \prime }}^{2}-2 y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime }+x^{2} = 0
\] |
[[_2nd_order, _missing_y]] |
✗ |
6.299 |
|