|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-3 y = \delta \left (t -2\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.298 |
|
|
\[
{}y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_linear, ‘class A‘]] |
✓ |
0.304 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.424 |
|
|
\[
{}y^{\prime \prime }+16 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.297 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -\frac {\pi }{2}\right )+\delta \left (t -\frac {3 \pi }{2}\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.349 |
|
|
\[
{}y^{\prime \prime }+y = \delta \left (t -2 \pi \right )+\delta \left (t -4 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.458 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } = \delta \left (t -1\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } = 1+\delta \left (t -2\right )
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.334 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+5 y = \delta \left (t -2 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.300 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+y = \delta \left (t -1\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.277 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime }+13 y = \delta \left (t -\pi \right )+\delta \left (t -3 \pi \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.523 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = {\mathrm e}^{t}+\delta \left (t -2\right )+\delta \left (t -4\right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.381 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.326 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }+10 y = \delta \left (t \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
0.261 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=4 x+8 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.615 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-7 y \\ y^{\prime }=5 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.605 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y-9 z \\ y^{\prime }=6 x-y \\ z^{\prime }=10 x+4 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
8.990 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+2 z \\ z^{\prime }=z-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
7.103 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+z+t -1 \\ y^{\prime }=2 x+y-z-3 t^{2} \\ z^{\prime }=x+y+z+t^{2}-t +2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.923 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y+{\mathrm e}^{-t} \sin \left (2 t \right ) \\ y^{\prime }=5 x+9 z+4 \,{\mathrm e}^{-t} \cos \left (2 t \right ) \\ z^{\prime }=y+6 z-{\mathrm e}^{-t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
214.013 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+2 y+{\mathrm e}^{t} \\ y^{\prime }=-x+3 y-{\mathrm e}^{t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.084 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=7 x+5 y-9 z-8 \,{\mathrm e}^{-2 t} \\ y^{\prime }=4 x+y+z+2 \,{\mathrm e}^{5 t} \\ z^{\prime }=-2 y+3 z+{\mathrm e}^{5 t}-3 \,{\mathrm e}^{-2 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
28.237 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y+2 z+{\mathrm e}^{-t}-3 t \\ y^{\prime }=3 x-4 y+z+2 \,{\mathrm e}^{-t}+t \\ z^{\prime }=-2 x+5 y+6 z+2 \,{\mathrm e}^{-t}-t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
209.684 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-7 y+4 \sin \left (t \right )+\left (t -4\right ) {\mathrm e}^{4 t} \\ y^{\prime }=x+y+8 \sin \left (t \right )+\left (2 t +1\right ) {\mathrm e}^{4 t} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
3.514 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.327 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+5 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+\frac {y}{4} \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.263 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+z \\ y^{\prime }=6 x-y \\ z^{\prime }=-x-2 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=x+y \\ z^{\prime }=-2 x-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.549 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=4 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.311 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.293 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.335 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+2 y \\ y^{\prime }=\frac {3 x}{4}-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.313 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=10 x-5 y \\ y^{\prime }=8 x-12 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.326 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+2 y \\ y^{\prime }=-3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.317 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-z \\ y^{\prime }=2 y \\ z^{\prime }=y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-7 y \\ y^{\prime }=5 x+10 y+4 z \\ z^{\prime }=5 y+2 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=x+2 y+z \\ z^{\prime }=3 y-z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.500 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+z \\ y^{\prime }=y \\ z^{\prime }=x+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.558 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-y \\ y^{\prime }=\frac {3 x}{4}-\frac {3 y}{2}+3 z \\ z^{\prime }=\frac {x}{8}+\frac {y}{4}-\frac {z}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.542 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+4 y+2 z \\ y^{\prime }=4 x-y-2 z \\ z^{\prime }=6 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.411 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 z \\ y^{\prime }=2 y \\ z^{\prime }=x+y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.495 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {9 x}{10}+\frac {21 y}{10}+\frac {16 z}{5} \\ y^{\prime }=\frac {7 x}{10}+\frac {13 y}{2}+\frac {21 z}{5} \\ z^{\prime }=\frac {11 x}{10}+\frac {17 y}{10}+\frac {17 z}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
76.548 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{3}-\frac {9 x_{4}}{5} \\ x_{2}^{\prime }=\frac {51 x_{2}}{10}-x_{4}+3 x_{5} \\ x_{3}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{4}^{\prime }=x_{2}-\frac {31 x_{3}}{10}+4 x_{4} \\ x_{5}^{\prime }=-\frac {14 x_{1}}{5}+\frac {3 x_{4}}{2}-x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
85.256 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=9 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.254 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-6 x+5 y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.306 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+3 y \\ y^{\prime }=-3 x+5 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.280 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=12 x-9 y \\ y^{\prime }=4 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.290 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y-z \\ y^{\prime }=x+y-z \\ z^{\prime }=x-y+z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.363 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+4 z \\ y^{\prime }=2 x+2 z \\ z^{\prime }=4 x+2 y+3 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.472 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+2 z \\ z^{\prime }=2 y+5 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.441 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=3 y+z \\ z^{\prime }=z-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.342 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+2 y-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.370 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+y \\ y^{\prime }=4 y+z \\ z^{\prime }=4 z \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.288 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=-x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=y \\ z^{\prime }=x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=6 x-y \\ y^{\prime }=5 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.387 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+y \\ y^{\prime }=-2 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.386 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+5 y \\ y^{\prime }=-2 x+6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.476 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-5 y \\ y^{\prime }=5 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-8 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=z \\ y^{\prime }=-z \\ z^{\prime }=y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y+2 z \\ y^{\prime }=3 x+6 z \\ z^{\prime }=-4 x-3 z \end {array}\right ]
\] |
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 |
✓ |
0.615 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+3 y-7 \\ y^{\prime }=-x-2 y+5 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x+9 y+2 \\ y^{\prime }=-x+11 y+6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.501 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-y^{2} = 0
\] |
[_separable] |
✓ |
2.394 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (2 x +3 y\right ) y^{\prime }+6 y = 0
\] |
[_quadrature] |
✓ |
1.791 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-5 x y y^{\prime }+6 y^{2} = 0
\] |
[_separable] |
✓ |
2.789 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}+y^{\prime } x -y^{2}-y = 0
\] |
[_separable] |
✓ |
2.352 |
|
|
\[
{}x {y^{\prime }}^{2}+\left (1-x^{2} y\right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
1.253 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x^{2} y+3\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_quadrature] |
✓ |
1.351 |
|
|
\[
{}x {y^{\prime }}^{2}-\left (y x +1\right ) y^{\prime }+y = 0
\] |
[_quadrature] |
✓ |
0.684 |
|
|
\[
{}{y^{\prime }}^{2}-x^{2} y^{2} = 0
\] |
[_separable] |
✓ |
2.139 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.312 |
|
|
\[
{}y {y^{\prime }}^{2}+\left (x -y^{2}\right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
2.814 |
|
|
\[
{}{y^{\prime }}^{2}-x y \left (x +y\right ) y^{\prime }+x^{3} y^{3} = 0
\] |
[_separable] |
✓ |
2.374 |
|
|
\[
{}\left (4 x -y\right ) {y^{\prime }}^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y = 0
\] |
[_quadrature] |
✓ |
3.532 |
|
|
\[
{}\left (x -y\right )^{2} {y^{\prime }}^{2} = y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.596 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (-1+x y^{2}\right ) y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
1.510 |
|
|
\[
{}\left (x^{2}+y^{2}\right )^{2} {y^{\prime }}^{2} = 4 x^{2} y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.492 |
|
|
\[
{}\left (x +y\right )^{2} {y^{\prime }}^{2}+\left (2 y^{2}+y x -x^{2}\right ) y^{\prime }+\left (-x +y\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.292 |
|
|
\[
{}x y \left (x^{2}+y^{2}\right ) \left ({y^{\prime }}^{2}-1\right ) = y^{\prime } \left (x^{4}+x^{2} y^{2}+y^{4}\right )
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.046 |
|
|
\[
{}x {y^{\prime }}^{3}-\left (x^{2}+x +y\right ) {y^{\prime }}^{2}+\left (x^{2}+y x +y\right ) y^{\prime }-y x = 0
\] |
[_quadrature] |
✓ |
1.638 |
|
|
\[
{}x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.732 |
|
|
\[
{}x {y^{\prime }}^{2}-2 y y^{\prime }+4 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.444 |
|
|
\[
{}3 x^{4} {y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.040 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.347 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.303 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.429 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}-4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.448 |
|
|
\[
{}4 y^{3} {y^{\prime }}^{2}+4 y^{\prime } x +y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
3.478 |
|
|
\[
{}{y^{\prime }}^{3}+x {y^{\prime }}^{2}-y = 0
\] |
[_dAlembert] |
✓ |
2.922 |
|
|
\[
{}y^{4} {y^{\prime }}^{3}-6 y^{\prime } x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
235.092 |
|
|
\[
{}{y^{\prime }}^{2}+x^{3} y^{\prime }-2 x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.517 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.354 |
|