|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )-2 y \sin \left (x \right )+\left ({\mathrm e}^{x} \cos \left (y\right )+2 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.529 |
|
|
\[
{}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
7.555 |
|
|
\[
{}y \,{\mathrm e}^{x y} \cos \left (2 x \right )-2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+2 x +\left (x \,{\mathrm e}^{x y} \cos \left (2 x \right )-3\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
36.629 |
|
|
\[
{}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.455 |
|
|
\[
{}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.692 |
|
|
\[
{}\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}} = 0
\] |
[_separable] |
✓ |
4.573 |
|
|
\[
{}2 x -y+\left (2 y-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.475 |
|
|
\[
{}9 x^{2}+y-1-\left (4 y-x \right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.830 |
|
|
\[
{}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.576 |
|
|
\[
{}\frac {\sin \left (y\right )}{y}-2 \,{\mathrm e}^{-x} \sin \left (x \right )+\frac {\left (\cos \left (y\right )+2 \,{\mathrm e}^{-x} \cos \left (x \right )\right ) y^{\prime }}{y} = 0
\] |
[NONE] |
✓ |
11.148 |
|
|
\[
{}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.200 |
|
|
\[
{}\left (x +2\right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.106 |
|
|
\[
{}3 x^{2} y+2 x y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
2.072 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{2 x}+y-1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.268 |
|
|
\[
{}\frac {y^{\prime }}{\frac {x}{y}-\sin \left (y\right )} = 0
\] |
[_quadrature] |
✓ |
0.686 |
|
|
\[
{}y+\left (2 x y-{\mathrm e}^{-2 y}\right ) y^{\prime } = 0
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.722 |
|
|
\[
{}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.364 |
|
|
\[
{}\frac {4 x^{3}}{y^{2}}+\frac {12}{y}+3 \left (\frac {x}{y^{2}}+4 y\right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.257 |
|
|
\[
{}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
1.430 |
|
|
\[
{}3 x y+y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.632 |
|
|
\[
{}y y^{\prime } = x +1
\] |
[_separable] |
✓ |
2.424 |
|
|
\[
{}\left (y^{4}+1\right ) y^{\prime } = x^{4}+1
\] |
[_separable] |
✓ |
1.350 |
|
|
\[
{}\frac {\left (3 x^{3}-x y^{2}\right ) y^{\prime }}{3 x^{2} y+y^{3}} = 1
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
23.175 |
|
|
\[
{}x \left (x -1\right ) y^{\prime } = y \left (1+y\right )
\] |
[_separable] |
✓ |
2.241 |
|
|
\[
{}\sqrt {x^{2}-y^{2}}+y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
53.517 |
|
|
\[
{}x y y^{\prime } = \left (x +y\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.644 |
|
|
\[
{}y^{\prime } = \frac {4 y-7 x}{5 x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.196 |
|
|
\[
{}y^{\prime } x -4 \sqrt {y^{2}-x^{2}} = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
49.102 |
|
|
\[
{}y^{\prime } = \frac {y^{4}+2 x y^{3}-3 x^{2} y^{2}-2 x^{3} y}{2 x^{2} y^{2}-2 x^{3} y-2 x^{4}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
17.121 |
|
|
\[
{}\left (y+x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime } = y \,{\mathrm e}^{\frac {x}{y}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.579 |
|
|
\[
{}x y y^{\prime } = x^{2}+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
11.495 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1548.904 |
|
|
\[
{}t y^{\prime }+y = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.976 |
|
|
\[
{}y^{\prime } = y \left (t y^{3}-1\right )
\] |
[_Bernoulli] |
✓ |
1.270 |
|
|
\[
{}y^{\prime }+\frac {3 y}{t} = t^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.384 |
|
|
\[
{}t^{2} y^{\prime }+2 t y-y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.444 |
|
|
\[
{}5 \left (t^{2}+1\right ) y^{\prime } = 4 t y \left (y^{3}-1\right )
\] |
[_separable] |
✓ |
39.544 |
|
|
\[
{}3 t y^{\prime }+9 y = 2 t y^{{5}/{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
72.078 |
|
|
\[
{}y^{\prime } = y+\sqrt {y}
\] |
[_quadrature] |
✓ |
2.434 |
|
|
\[
{}y^{\prime } = r y-k^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.378 |
|
|
\[
{}y^{\prime } = a y+b y^{3}
\] |
[_quadrature] |
✓ |
1.679 |
|
|
\[
{}y^{\prime }+3 t y = 4-4 t^{2}+y^{2}
\] |
[_Riccati] |
✓ |
1.636 |
|
|
\[
{}\left (3 x-y \right ) x^{\prime }+9 y -2 x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.476 |
|
|
\[
{}1 = \left (3 \,{\mathrm e}^{y}-2 x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
1.412 |
|
|
\[
{}y^{\prime }-4 \,{\mathrm e}^{x} y^{2} = y
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.464 |
|
|
\[
{}y^{\prime } x +\left (x +1\right ) y = x
\] |
[_linear] |
✓ |
1.109 |
|
|
\[
{}y^{\prime } = \frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y}
\] |
[_Bernoulli] |
✓ |
40.299 |
|
|
\[
{}\frac {\sqrt {x}\, y^{\prime }}{y} = 1
\] |
[_separable] |
✓ |
1.638 |
|
|
\[
{}5 x y^{2}+5 y+\left (5 x^{2} y+5 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.137 |
|
|
\[
{}2 x y y^{\prime }+\ln \left (x \right ) = -y^{2}-1
\] |
[_exact, _Bernoulli] |
✓ |
1.442 |
|
|
\[
{}\left (2-x \right ) y^{\prime } = y+2 \left (2-x \right )^{5}
\] |
[_linear] |
✓ |
1.513 |
|
|
\[
{}y^{\prime } x = -\frac {1}{\ln \left (x \right )}
\] |
[_quadrature] |
✓ |
0.483 |
|
|
\[
{}x^{\prime } = \frac {2 x y +x^{2}}{3 y^{2}+2 x y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.573 |
|
|
\[
{}4 x y y^{\prime } = 8 x^{2}+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.928 |
|
|
\[
{}y^{\prime }+y-y^{{1}/{4}} = 0
\] |
[_quadrature] |
✓ |
3.949 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=x+4 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.513 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+\sin \left (t \right ) \\ y^{\prime }=-x+y-\cos \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.146 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 t x+y \\ y^{\prime }=3 x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.054 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y+4 \\ y^{\prime }=-2 x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.698 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.700 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+t y \\ y^{\prime }=t x-y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.055 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y+4 \\ y^{\prime }=-2 x+\sin \left (t \right ) y \end {array}\right ]
\] |
system_of_ODEs |
✗ |
0.059 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.475 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.403 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.454 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+2 \sin \left (t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.678 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-4 y+2 t \\ y^{\prime }=x-3 y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.559 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x+y+1 \\ y^{\prime }=x+y-3 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.758 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y-4 \\ y^{\prime }=x-y-6 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.702 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4}+8 \\ y^{\prime }=\frac {x}{2}+y-\frac {23}{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.625 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y-11 \\ y^{\prime }=-5 x+4 y-35 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.608 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y-3 \\ y^{\prime }=-x+y+1 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.705 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+4 y-35 \\ y^{\prime }=-2 x+y-11 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.612 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.424 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.421 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.412 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.401 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {5 x}{4}+\frac {3 y}{4} \\ y^{\prime }=\frac {3 x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.392 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {3 x}{4}-\frac {7 y}{4} \\ y^{\prime }=\frac {x}{4}+\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.404 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-\frac {x}{4}-\frac {3 y}{4} \\ y^{\prime }=\frac {x}{2}+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.405 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.398 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+6 y \\ y^{\prime }=-x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.385 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=3 x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.506 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-5 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.522 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.554 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.458 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.453 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-\frac {5 y}{2} \\ y^{\prime }=\frac {9 x}{5}-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.572 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=5 x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.496 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-5 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-x-4 y \\ y^{\prime }=x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.521 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.497 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.535 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+2 y \\ y^{\prime }=-x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.589 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=\frac {3 x}{4}-2 y \\ y^{\prime }=x-\frac {5 y}{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.485 |
|