|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.081 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.079 |
|
|
\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.086 |
|
|
\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.092 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.223 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.228 |
|
|
\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.233 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.223 |
|
|
\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.285 |
|
|
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.283 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.281 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.292 |
|
|
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.107 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.109 |
|
|
\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.219 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.219 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.245 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.245 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.227 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.225 |
|
|
\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
✓ |
0.188 |
|
|
\[
{}y^{\prime } = f \left (x \right )
\] |
[_quadrature] |
✓ |
0.175 |
|
|
\[
{}y^{\prime } = f \left (y\right )
\] |
[_quadrature] |
✓ |
0.936 |
|
|
\[
{}y^{\prime } = f \left (x \right ) g \left (y\right )
\] |
[_separable] |
✓ |
1.073 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right )
\] |
[_linear] |
✓ |
1.460 |
|
|
\[
{}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n}
\] |
[_Bernoulli] |
✓ |
2.284 |
|
|
\[
{}y^{\prime } = f \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
1.418 |
|
|
\[
{}y^{\prime } = a y^{2}+b x +c
\] |
[_Riccati] |
✓ |
1.289 |
|
|
\[
{}y^{\prime } = y^{2}-a^{2} x^{2}+3 a
\] |
[_Riccati] |
✓ |
1.942 |
|
|
\[
{}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c
\] |
[_Riccati] |
✓ |
9.487 |
|
|
\[
{}y^{\prime } = a y^{2}+b \,x^{n}
\] |
[[_Riccati, _special]] |
✓ |
1.720 |
|
|
\[
{}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n}
\] |
[_Riccati] |
✗ |
768.667 |
|
|
\[
{}y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1}
\] |
[_Riccati] |
✓ |
3.789 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2}
\] |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
2.300 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m}
\] |
[_Riccati] |
✓ |
2.281 |
|
|
\[
{}y^{\prime } = y^{2}+k \left (a x +b \right )^{n} \left (c x +d \right )^{-n -4}
\] |
[_Riccati] |
✗ |
10.591 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m}
\] |
[_Riccati] |
✗ |
413.367 |
|
|
\[
{}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c
\] |
[_Riccati] |
✓ |
55.196 |
|
|
\[
{}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
3.780 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.893 |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right )
\] |
[_rational, _Riccati] |
✓ |
3.007 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c
\] |
[_rational, _Riccati] |
✓ |
2.590 |
|
|
\[
{}x^{2} y^{\prime } = y^{2} x^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4}
\] |
[_Riccati] |
✗ |
5.095 |
|
|
\[
{}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
13.347 |
|
|
\[
{}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2}
\] |
[_rational, [_Riccati, _special]] |
✓ |
3.404 |
|
|
\[
{}a \,x^{2} \left (-1+x \right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0
\] |
[_rational, _Riccati] |
✓ |
4.817 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0
\] |
[_rational, _Riccati] |
✓ |
3.604 |
|
|
\[
{}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d
\] |
[_Riccati] |
✓ |
3.558 |
|
|
\[
{}\left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2}
\] |
[_rational, _Riccati] |
✓ |
4.545 |
|
|
\[
{}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0
\] |
[_rational, _Riccati] |
✓ |
5.698 |
|
|
\[
{}y^{\prime } = a y^{2}+b y+c x +k
\] |
[_Riccati] |
✓ |
1.596 |
|
|
\[
{}y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1}
\] |
[_Riccati] |
✓ |
2.839 |
|
|
\[
{}y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1}
\] |
[_Riccati] |
✓ |
4.050 |
|
|
\[
{}y^{\prime } = y^{2}+\left (\alpha x +\beta \right ) y+a \,x^{2}+b x +c
\] |
[_Riccati] |
✓ |
39.063 |
|
|
\[
{}y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2}
\] |
[_Riccati] |
✗ |
4.004 |
|
|
\[
{}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{n +m +1}-a \,x^{m}
\] |
[_Riccati] |
✗ |
5.790 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n}
\] |
[_Riccati] |
✗ |
5.211 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1}
\] |
[_Riccati] |
✓ |
7.361 |
|
|
\[
{}y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m}
\] |
[_Riccati] |
✓ |
13.411 |
|
|
\[
{}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k}
\] |
[_Riccati] |
✗ |
9.790 |
|
|
\[
{}x y^{\prime } = a y^{2}+b y+c \,x^{2 b}
\] |
[_rational, _Riccati] |
✓ |
2.872 |
|
|
\[
{}x y^{\prime } = a y^{2}+b y+c \,x^{n}
\] |
[_rational, _Riccati] |
✓ |
2.454 |
|
|
\[
{}x y^{\prime } = a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n}
\] |
[_rational, _Riccati] |
✓ |
3.519 |
|
|
\[
{}x y^{\prime } = x y^{2}+a y+b \,x^{n}
\] |
[_rational, _Riccati] |
✓ |
2.503 |
|
|
\[
{}x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
6.638 |
|
|
\[
{}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.650 |
|
|
\[
{}x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m}
\] |
[_rational, _Riccati] |
✓ |
2.470 |
|
|
\[
{}x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m}
\] |
[_rational, _Riccati] |
✓ |
2.528 |
|
|
\[
{}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m}
\] |
[_rational, _Riccati] |
✓ |
3.370 |
|
|
\[
{}x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c
\] |
[_rational, _Riccati] |
✓ |
4.328 |
|
|
\[
{}x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{m +n}-n \right ) y+c \,x^{m}
\] |
[_rational, _Riccati] |
✓ |
41.580 |
|
|
\[
{}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
21.223 |
|
|
\[
{}\left (a x +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
3.499 |
|
|
\[
{}2 x^{2} y^{\prime } = 2 y^{2}+x y-2 a^{2} x
\] |
[_rational, _Riccati] |
✓ |
1.446 |
|
|
\[
{}2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 a^{2} x
\] |
[_rational, _Riccati] |
✓ |
1.972 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.351 |
|
|
\[
{}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{2}+b x \right ) y+\alpha \,x^{2}+\beta x +\gamma
\] |
[_rational, _Riccati] |
✓ |
7.492 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{n}+s
\] |
[_rational, _Riccati] |
✓ |
3.045 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n}
\] |
[_rational, _Riccati] |
✓ |
4.397 |
|
|
\[
{}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma
\] |
[_rational, _Riccati] |
✓ |
35.227 |
|
|
\[
{}x^{2} y^{\prime } = \left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2}
\] |
[_rational, _Riccati] |
✗ |
597.533 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 x y+1\right ) = 0
\] |
[_rational, _Riccati] |
✗ |
7.472 |
|
|
\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha } = 0
\] |
[_rational, _Riccati] |
✓ |
472.467 |
|
|
\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma = 0
\] |
[_rational, _Riccati] |
✓ |
505.818 |
|
|
\[
{}\left (a \,x^{2}+b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.865 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
4.966 |
|
|
\[
{}\left (a \,x^{2}+b x +c \right ) y^{\prime } = y^{2}+\left (a x +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +\lambda c
\] |
[_rational, _Riccati] |
✗ |
480.184 |
|
|
\[
{}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2}
\] |
[_rational, _Riccati] |
✓ |
51.929 |
|
|
\[
{}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0}
\] |
[_rational, _Riccati] |
✓ |
46.097 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.325 |
|
|
\[
{}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0} = 0
\] |
[_rational, _Riccati] |
✓ |
23.987 |
|
|
\[
{}x^{3} y^{\prime } = a \,x^{3} y^{2}+\left (b \,x^{2}+c \right ) y+s x
\] |
[_rational, _Riccati] |
✓ |
11.829 |
|
|
\[
{}x^{3} y^{\prime } = a \,x^{3} y^{2}+x \left (b x +c \right ) y+\alpha x +\beta
\] |
[_rational, _Riccati] |
✓ |
5.363 |
|
|
\[
{}x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x = 0
\] |
[_rational, _Riccati] |
✓ |
5.281 |
|
|
\[
{}x^{2} \left (x +a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+\alpha x +\beta = 0
\] |
[_rational, _Riccati] |
✓ |
6.910 |
|
|
\[
{}\left (a \,x^{2}+b x +e \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.213 |
|
|
\[
{}x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s = 0
\] |
[_rational, _Riccati] |
✓ |
7.786 |
|
|
\[
{}a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s = 0
\] |
[_rational, _Riccati] |
✗ |
6.226 |
|
|
\[
{}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+b \,x^{n} y+c \,x^{m}+d
\] |
[_Riccati] |
✓ |
4.492 |
|
|
\[
{}x \left (a \,x^{k}+b \right ) y^{\prime } = \alpha \,x^{n} y^{2}+\left (\beta -a n \,x^{k}\right ) y+\gamma \,x^{-n}
\] |
[_rational, _Riccati] |
✓ |
43.495 |
|