|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\sqrt {x^{2}-y^{2}}+y = x y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
90.371 |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.699 |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.780 |
|
|
\[
{}x y^{\prime }-4 \sqrt {y^{2}-x^{2}} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
59.152 |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
17.947 |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.305 |
|
|
\[
{}x y y^{\prime } = y^{2}+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
12.277 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1195.576 |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.770 |
|
|
\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
[_Bernoulli] |
✓ |
1.249 |
|
|
\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.197 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.471 |
|
|
\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
[_separable] |
✓ |
39.752 |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
13.794 |
|
|
\[
{}y^{\prime } = y+\sqrt {y}
\] |
[_quadrature] |
✓ |
2.292 |
|
|
\[
{}y^{\prime } = r y-k^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.426 |
|
|
\[
{}y^{\prime } = a y+b y^{3}
\] |
[_quadrature] |
✓ |
1.896 |
|
|
\[
{}y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\] |
[_Riccati] |
✓ |
1.660 |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.518 |
|
|
\[
{}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.330 |
|
|
\[
{}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.347 |
|
|
\[
{}x y^{\prime }+\left (x +1\right ) y = x
\] |
[_linear] |
✓ |
1.080 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\] |
[_Bernoulli] |
✓ |
40.111 |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
[_separable] |
✓ |
1.439 |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.671 |
|
|
\[
{}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\] |
[_exact, _Bernoulli] |
✓ |
1.506 |
|
|
\[
{}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\] |
[_linear] |
✓ |
1.319 |
|
|
\[
{}x y^{\prime } = -\frac {1}{\ln \left (x \right )}
\] |
[_quadrature] |
✓ |
0.374 |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.388 |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.833 |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
[_quadrature] |
✓ |
4.138 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+\sin \left (t \right ) \\ y^{\prime }=-x+y-\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.211 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x t +y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.050 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+4 \\ y^{\prime }=-2 x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.642 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.636 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+t y \\ y^{\prime }=x t -y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.048 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 \\ y^{\prime }=-2 x+\sin \left (t \right ) y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.049 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.388 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.366 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+2 \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.714 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+2 t \\ y^{\prime }=x-3 y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.571 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+1 \\ y^{\prime }=x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.703 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y-4 \\ y^{\prime }=x-y-6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.704 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }=\frac {x}{2}+y-\frac {23}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.553 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-11 \\ y^{\prime }=-5 x+4 y-35 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.550 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-3 \\ y^{\prime }=-x+y+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.613 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y-35 \\ y^{\prime }=-2 x+y-11 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.546 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.332 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.350 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {3 x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }=\frac {x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.327 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.334 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+6 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.309 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.459 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.378 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.385 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-\frac {5 y}{2} \\ y^{\prime }=\frac {9 x}{5}-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.456 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-5 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.400 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.437 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.519 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.527 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {3 x}{4}-2 y \\ y^{\prime }=x-\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.403 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {4 x}{5}+2 y \\ y^{\prime }=-x+\frac {6 y}{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.399 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+y \\ y^{\prime }=-x+a y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.325 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 y \\ y^{\prime }=x+a y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.600 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=a x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.514 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=a x+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.508 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+a y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+a y \\ y^{\prime }=-6 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=a x+10 y \\ y^{\prime }=-x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.648 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x+a y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} i^{\prime }=\frac {i}{2}-\frac {v}{8} \\ v^{\prime }=2 i-\frac {v}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.282 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.308 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.300 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{2}+y \\ y^{\prime }=-\frac {x}{4}-\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.316 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.295 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-\frac {y}{2} \\ y^{\prime }=2 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.318 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {5 x}{2}+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}+\frac {y}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.440 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {3 y}{2} \\ y^{\prime }=-\frac {3 x}{2}-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=-\frac {3 x}{4}-\frac {y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.447 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+\frac {5 y}{2} \\ y^{\prime }=-\frac {5 x}{2}+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.442 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+\frac {y}{2} \\ y^{\prime }=-\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.409 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|