|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 y \\ z^{\prime }=y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.395 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-7 y \\ y^{\prime }=5 x+10 y+4 z \\ z^{\prime }=5 y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.479 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x+2 y+z \\ z^{\prime }=3 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.468 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=y \\ z^{\prime }=x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.345 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.488 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y+2 z \\ y^{\prime }=4 x-y-2 z \\ z^{\prime }=6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.535 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 z \\ y^{\prime }=2 y \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
62.882 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
87.845 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=9 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.333 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+5 y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.429 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=-3 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.427 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x-9 y \\ y^{\prime }=4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y-z \\ y^{\prime }=x+y-z \\ z^{\prime }=x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.358 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.409 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+2 z \\ z^{\prime }=2 y+5 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.413 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 y+z \\ z^{\prime }=z-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.351 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+2 y-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.343 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y \\ y^{\prime }=4 y+z \\ z^{\prime }=4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=-x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=y \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.539 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.511 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.530 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.554 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.523 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.538 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.403 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.822 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-12 y-14 z \\ y^{\prime }=x+2 y-3 z \\ z^{\prime }=x+y-2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.684 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.562 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.575 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
2.565 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
0.459 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
1.062 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+x y^{\prime }-y^{2}-y = 0
\] |
[_separable] |
✓ |
0.778 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.625 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_quadrature] |
✓ |
0.487 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (1+x y\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.448 |
|
|
\[
{}{y^{\prime }}^{2}-y^{2} x^{2} = 0
\] |
[_separable] |
✓ |
2.334 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.628 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.504 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
0.895 |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[_quadrature] |
✓ |
0.724 |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.323 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x y^{2}-1\right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.528 |
|
|
\[
{}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 y^{2} x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
45.930 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+x y-x^{2}\right ) y^{\prime }+y \left (y-x \right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.572 |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+y^{2} x^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
418.068 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+x y+y\right ) y^{\prime }-x y = 0
\] |
[_quadrature] |
✓ |
0.825 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.511 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.344 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.725 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.438 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.387 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.737 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.297 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}+4 x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.010 |
|
|
\[
{}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\] |
[_dAlembert] |
✓ |
2.907 |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
108.414 |
|
|
\[
{}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.871 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.715 |
|
|
\[
{}2 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+x^{4} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
120.142 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.394 |
|
|
\[
{}y = x y^{\prime }+k {y^{\prime }}^{2}
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.480 |
|
|
\[
{}x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.869 |
|
|
\[
{}x^{4} {y^{\prime }}^{2}+2 x^{3} y y^{\prime }-4 = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.203 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.412 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.775 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (x -y\right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _dAlembert] |
✓ |
0.514 |
|
|
\[
{}y^{\prime } \left (x y^{\prime }-y+k \right )+a = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
0.474 |
|
|
\[
{}x^{6} {y^{\prime }}^{3}-3 x y^{\prime }-3 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
10.691 |
|
|
\[
{}y = x^{6} {y^{\prime }}^{3}-x y^{\prime }
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
13.661 |
|
|
\[
{}x {y^{\prime }}^{4}-2 y {y^{\prime }}^{3}+12 x^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.431 |
|
|
\[
{}x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+1 = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.549 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.440 |
|
|
\[
{}2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.425 |
|
|
\[
{}2 {y^{\prime }}^{2}+x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.588 |
|
|
\[
{}{y^{\prime }}^{3}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.444 |
|
|
\[
{}4 x {y^{\prime }}^{2}-3 y y^{\prime }+3 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _dAlembert] |
✓ |
0.483 |
|
|
\[
{}{y^{\prime }}^{3}-x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.432 |
|
|
\[
{}5 {y^{\prime }}^{2}+6 x y^{\prime }-2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.465 |
|
|
\[
{}2 x {y^{\prime }}^{2}+\left (2 x -y\right ) y^{\prime }+1-y = 0
\] |
[_rational, _dAlembert] |
✓ |
1.245 |
|
|
\[
{}5 {y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.463 |
|
|
\[
{}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.467 |
|
|
\[
{}y = x y^{\prime }+x^{3} {y^{\prime }}^{2}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.163 |
|
|
\[
{}y^{\prime \prime } = x {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.481 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.435 |
|
|
\[
{}x^{2} y^{\prime \prime }+{y^{\prime }}^{2}-2 x y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.483 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
1.079 |
|
|
\[
{}y^{2} y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.355 |
|
|
\[
{}\left (y+1\right ) y^{\prime \prime } = {y^{\prime }}^{2}
\] |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
0.325 |
|
|
\[
{}2 a y^{\prime \prime }+{y^{\prime }}^{3} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.719 |
|
|
\[
{}x y^{\prime \prime } = y^{\prime }+x^{5}
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.375 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.440 |
|
|
\[
{}y^{\prime \prime } = 2 y {y^{\prime }}^{3}
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.217 |
|
|
\[
{}y y^{\prime \prime }+{y^{\prime }}^{3}-{y^{\prime }}^{2} = 0
\] |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
0.463 |
|
|
\[
{}y^{\prime \prime }+\beta ^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.649 |
|