|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x^{\prime }=y-x \\ y^{\prime }=x-2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.531 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=3 y-3 x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.631 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=3 x-4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.463 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-y \\ y^{\prime }=3 x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.284 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.314 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.283 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=6 x+3 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.365 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.350 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=2 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.237 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=4 x-y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.436 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=5 x-4 y \\ y^{\prime }=x+y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.318 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=9 y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.375 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.422 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=-2 x+4 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.319 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x-y+1 \\ y^{\prime }=x+y+2 \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.637 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=-5 x+3 y+{\mathrm e}^{-t} \\ y^{\prime }=2 x-10 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.541 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x+\cos \left (w t \right ) \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.710 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=3 x+2 y+3 \\ y^{\prime }=7 x+5 y+2 t \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.934 |
|
|
\[
{}\left [\begin {array}{c} x^{\prime }=x-3 y \\ y^{\prime }=3 x+7 y \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.308 |
|
|
\[
{}y^{\prime }+y = x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.109 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.827 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.168 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 x y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.117 |
|
|
\[
{}2 x y y^{\prime }+x^{2}+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
4.052 |
|
|
\[
{}x y^{\prime }+y = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.645 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.550 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.144 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-8 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.834 |
|
|
\[
{}y^{\prime \prime \prime }-2 y^{\prime \prime }-4 y^{\prime }+8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.070 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-10 x y^{\prime }-8 y = 0
\] |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime }+2 y = 6 \,{\mathrm e}^{x}+4 x \,{\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.507 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+4 y = -8 \sin \left (2 x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.358 |
|
|
\[
{}{y^{\prime }}^{2}-4 y = 0
\] |
[_quadrature] |
✓ |
0.622 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.460 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.811 |
|
|
\[
{}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.894 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.472 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.576 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✗ |
1.583 |
|
|
\[
{}y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.391 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.216 |
|
|
\[
{}y^{\prime } = x^{2} \sin \left (y\right )
\] |
[_separable] |
✓ |
3.565 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{-2+x}
\] |
[_separable] |
✓ |
2.224 |
|
|
\[
{}y^{\prime } = y^{{1}/{3}}
\] |
[_quadrature] |
✓ |
1.664 |
|
|
\[
{}3 x +2 y+\left (2 x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.977 |
|
|
\[
{}y^{2}+3+\left (2 x y-4\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.445 |
|
|
\[
{}2 x y+1+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.277 |
|
|
\[
{}3 x^{2} y+2-\left (x^{3}+y\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
1.230 |
|
|
\[
{}6 x y+2 y^{2}-5+\left (3 x^{2}+4 x y-6\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.587 |
|
|
\[
{}y \sec \left (x \right )^{2}+\sec \left (x \right ) \tan \left (x \right )+\left (\tan \left (x \right )+2 y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.253 |
|
|
\[
{}\frac {x}{y^{2}}+x +\left (\frac {x^{2}}{y^{3}}+y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.352 |
|
|
\[
{}\frac {\left (2 s-1\right ) s^{\prime }}{t}+\frac {s-s^{2}}{t^{2}} = 0
\] |
[_separable] |
✓ |
3.338 |
|
|
\[
{}\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.892 |
|
|
\[
{}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.631 |
|
|
\[
{}3 x^{2} y^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
5.537 |
|
|
\[
{}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
77.280 |
|
|
\[
{}y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.225 |
|
|
\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.288 |
|
|
\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
4.467 |
|
|
\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.179 |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.228 |
|
|
\[
{}y+x \left (y^{2}+x^{2}\right )^{2}+\left (y \left (y^{2}+x^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.835 |
|
|
\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.371 |
|
|
\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.358 |
|
|
\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.273 |
|
|
\[
{}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.328 |
|
|
\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
[_separable] |
✓ |
2.495 |
|
|
\[
{}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0
\] |
[_separable] |
✓ |
2.538 |
|
|
\[
{}\left (4+x \right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.219 |
|
|
\[
{}x +y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.188 |
|
|
\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.914 |
|
|
\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.676 |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.095 |
|
|
\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
8.107 |
|
|
\[
{}x^{3}+y^{2} \sqrt {y^{2}+x^{2}}-x y \sqrt {y^{2}+x^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.020 |
|
|
\[
{}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
18.233 |
|
|
\[
{}y+2+y \left (4+x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.718 |
|
|
\[
{}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.181 |
|
|
\[
{}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.121 |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
5.834 |
|
|
\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.626 |
|
|
\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
130.185 |
|
|
\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.738 |
|
|
\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.910 |
|
|
\[
{}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
54.919 |
|
|
\[
{}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.031 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
[_linear] |
✓ |
1.381 |
|
|
\[
{}x^{4} y^{\prime }+2 x^{3} y = 1
\] |
[_linear] |
✓ |
1.240 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.544 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.143 |
|
|
\[
{}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}}
\] |
[_separable] |
✓ |
1.181 |
|
|
\[
{}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u
\] |
[_separable] |
✓ |
1.312 |
|
|
\[
{}x y^{\prime }+\frac {\left (2 x +1\right ) y}{x +1} = x -1
\] |
[_linear] |
✓ |
1.334 |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y = x -1
\] |
[_linear] |
✓ |
1.509 |
|
|
\[
{}x y^{\prime }+x y+y-1 = 0
\] |
[_linear] |
✓ |
1.035 |
|
|
\[
{}y+\left (x y^{2}+x -y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.213 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.527 |
|