|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\(\left [\begin {array}{cc} 6 & -10 \\ 2 & -3 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.126 |
|
|
\(\left [\begin {array}{cc} 11 & -15 \\ 6 & -8 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.127 |
|
|
\(\left [\begin {array}{cc} -1 & 4 \\ -1 & 3 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.075 |
|
|
\(\left [\begin {array}{cc} 3 & -1 \\ 1 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.068 |
|
|
\(\left [\begin {array}{cc} 5 & 1 \\ -9 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.077 |
|
|
\(\left [\begin {array}{cc} 11 & 9 \\ -16 & -13 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.083 |
|
|
\(\left [\begin {array}{ccc} 1 & 3 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.129 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ 2 & -2 & 1 \\ 2 & -2 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.154 |
|
|
\(\left [\begin {array}{ccc} 3 & -3 & 1 \\ 2 & -2 & 1 \\ 0 & 0 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.148 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 0 \\ 0 & 1 & 0 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.139 |
|
|
\(\left [\begin {array}{ccc} 7 & -8 & 3 \\ 6 & -7 & 3 \\ 2 & -2 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.196 |
|
|
\(\left [\begin {array}{ccc} 6 & -5 & 2 \\ 4 & -3 & 2 \\ 2 & -2 & 3 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.217 |
|
|
\(\left [\begin {array}{ccc} 1 & 1 & -1 \\ -2 & 4 & -1 \\ -4 & 4 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.19 |
|
|
\(\left [\begin {array}{ccc} 2 & 0 & 0 \\ -6 & 11 & 2 \\ 6 & -15 & 0 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.209 |
|
|
\(\left [\begin {array}{ccc} 0 & 1 & 0 \\ -1 & 2 & 0 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.087 |
|
|
\(\left [\begin {array}{ccc} 2 & -2 & 1 \\ -1 & 2 & 0 \\ -5 & 7 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.085 |
|
|
\(\left [\begin {array}{ccc} -2 & 4 & -1 \\ -3 & 5 & -1 \\ -1 & 1 & 1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.131 |
|
|
\(\left [\begin {array}{ccc} 3 & -2 & 1 \\ 1 & 0 & 1 \\ -1 & 1 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.131 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & -2 & 0 \\ 0 & 1 & -2 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.145 |
|
|
\(\left [\begin {array}{cccc} 1 & 0 & 0 & 1 \\ 0 & 1 & 0 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.141 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 0 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.129 |
|
|
\(\left [\begin {array}{cccc} 1 & 1 & 0 & 1 \\ 0 & 1 & 1 & 1 \\ 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.126 |
|
|
\(\left [\begin {array}{ccccc} 2 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 0 & 0 \\ 0 & 0 & 0 & 2 & 1 \\ 0 & 0 & 0 & 0 & 2 \end {array}\right ]\) |
Eigenvectors |
N/A |
✓ |
N/A |
0.093 |
|
|
\[ {}y^{\prime } = f \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.192 |
|
|
\[ {}y^{\prime } = f \left (y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.25 |
|
|
\[ {}y^{\prime } = f \left (x \right ) g \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.701 |
|
|
\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{0} \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.224 |
|
|
\[ {}g \left (x \right ) y^{\prime } = f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = f \left (\frac {y}{x}\right ) \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.033 |
|
|
\[ {}y^{\prime } = a y^{2}+b x +c \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.483 |
|
|
\[ {}y^{\prime } = y^{2}-a^{2} x^{2}+3 a \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.68 |
|
|
\[ {}y^{\prime } = y^{2}+a^{2} x^{2}+b x +c \] |
riccati |
[_Riccati] |
✓ |
✓ |
14.279 |
|
|
\[ {}y^{\prime } = a y^{2}+b \,x^{n} \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
2.231 |
|
|
\[ {}y^{\prime } = y^{2}+a n \,x^{n -1}-a^{2} x^{2 n} \] |
riccati |
[_Riccati] |
✓ |
✓ |
118.678 |
|
|
\[ {}y^{\prime } = a y^{2}+b \,x^{2 n}+c \,x^{n -1} \] |
riccati |
[_Riccati] |
✓ |
✓ |
36.872 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{-n -2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.179 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.477 |
|
|
\[ {}y^{\prime } = y^{2}+k \left (x a +b \right )^{n} \left (c x +d \right )^{-n -4} \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.879 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b m \,x^{m -1}-a \,b^{2} x^{n +2 m} \] |
riccati |
[_Riccati] |
✓ |
✓ |
128.141 |
|
|
\[ {}y^{\prime } = \left (a \,x^{2 n}+b \,x^{n -1}\right ) y^{2}+c \] |
riccati |
[_Riccati] |
✓ |
✓ |
90.599 |
|
|
\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} x +b_{0} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
94.806 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
4.039 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}-a^{2} x^{4}+a \left (1-2 b \right ) x^{2}-b \left (b +1\right ) \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.519 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b \,x^{n}+c \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
4.32 |
|
|
\[ {}x^{2} y^{\prime } = x^{2} y^{2}+a \,x^{2 m} \left (b \,x^{m}+c \right )^{n}-\frac {n^{2}}{4}+\frac {1}{4} \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.649 |
|
|
\[ {}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+a_{0} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
143.639 |
|
|
\[ {}x^{4} y^{\prime } = -x^{4} y^{2}-a^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.489 |
|
|
\[ {}a \,x^{2} \left (-1+x \right )^{2} \left (y^{\prime }+\lambda y^{2}\right )+b \,x^{2}+c x +s = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
7.046 |
|
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, _Riccati] |
✓ |
✓ |
6.493 |
|
|
\[ {}x^{n +1} y^{\prime } = a \,x^{2 n} y^{2}+c \,x^{m}+d \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.091 |
|
|
\[ {}\left (a \,x^{n}+b \right ) y^{\prime } = b y^{2}+a \,x^{n -2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
5.682 |
|
|
\[ {}\left (a \,x^{n}+b \,x^{m}+c \right ) \left (y^{\prime }-y^{2}\right )+a n \left (n -1\right ) x^{n -2}+b m \left (m -1\right ) x^{m -2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
7.027 |
|
|
\[ {}y^{\prime } = a y^{2}+b y+c x +k \] |
riccati |
[_Riccati] |
✓ |
✓ |
2.887 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y+a \,x^{n -1} \] |
riccati |
[_Riccati] |
✓ |
✓ |
130.475 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y+b \,x^{n -1} \] |
riccati |
[_Riccati] |
✓ |
✓ |
7.266 |
|
|
\[ {}y^{\prime } = y^{2}+\left (\alpha x +\beta \right ) y+x^{2} a +b x +c \] |
riccati |
[_Riccati] |
✓ |
✓ |
67.095 |
|
|
\[ {}y^{\prime } = y^{2}+a \,x^{n} y-a b \,x^{n}-b^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
4.001 |
|
|
\[ {}y^{\prime } = -\left (n +1\right ) x^{n} y^{2}+a \,x^{1+m +n}-a \,x^{m} \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.684 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+b c \,x^{m}-a \,c^{2} x^{n} \] |
riccati |
[_Riccati] |
✓ |
✓ |
4.307 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}-a \,x^{n} \left (b \,x^{m}+c \right ) y+b m \,x^{m -1} \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.657 |
|
|
\[ {}y^{\prime } = -a n \,x^{n -1} y^{2}+c \,x^{m} \left (a \,x^{n}+b \right ) y-c \,x^{m} \] |
riccati |
[_Riccati] |
✓ |
✓ |
31.73 |
|
|
\[ {}y^{\prime } = a \,x^{n} y^{2}+b \,x^{m} y+c k \,x^{k -1}-b c \,x^{m +k}-a \,c^{2} x^{n +2 k} \] |
riccati |
[_Riccati] |
✓ |
✓ |
9.673 |
|
|
\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{2 b} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.538 |
|
|
\[ {}x y^{\prime } = a y^{2}+b y+c \,x^{n} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.43 |
|
|
\[ {}x y^{\prime } = a y^{2}+\left (n +b \,x^{n}\right ) y+c \,x^{2 n} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
4.291 |
|
|
\[ {}x y^{\prime } = x y^{2}+a y+b \,x^{n} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
4.086 |
|
|
\[ {}x y^{\prime }+a_{3} x y^{2}+a_{2} y+a_{1} x +a_{0} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
7.144 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{-n} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
3.868 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+m y-a \,b^{2} x^{n +2 m} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.948 |
|
|
\[ {}x y^{\prime } = x^{2 n} y^{2}+\left (m -n \right ) y+x^{2 m} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.868 |
|
|
\[ {}x y^{\prime } = a \,x^{n} y^{2}+b y+c \,x^{m} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
4.839 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n} y^{2}+\left (b \,x^{n}-n \right ) y+c \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.958 |
|
|
\[ {}x y^{\prime } = a \,x^{2 n +m} y^{2}+\left (b \,x^{m +n}-n \right ) y+c \,x^{m} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
5.187 |
|
|
\[ {}\left (a_{2} x +b_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (a_{1} x +b_{1} \right ) y+a_{0} x +b_{0} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
33.569 |
|
|
\[ {}\left (x a +c \right ) y^{\prime } = \alpha \left (b x +a y\right )^{2}+\beta \left (b x +a y\right )-b x +\gamma \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
5.273 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 y^{2}+x y-2 x \,a^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.02 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 y^{2}+3 x y-2 x \,a^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.115 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
4.879 |
|
|
\[ {}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (x^{2} a +b x \right ) y+\alpha \,x^{2}+\beta x +\gamma \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
123.02 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{n}+s \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
5.068 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}+b x y+c \,x^{2 n}+s \,x^{n} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
7.152 |
|
|
\[ {}x^{2} y^{\prime } = c \,x^{2} y^{2}+\left (a \,x^{n}+b \right ) x y+\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
161.362 |
|
|
\[ {}x^{2} y^{\prime } = \left (\alpha \,x^{2 n}+\beta \,x^{n}+\gamma \right ) y^{2}+\left (a \,x^{n}+b \right ) x y+c \,x^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
70.098 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+\lambda \left (y^{2}-2 x y+1\right ) = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.589 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\frac {b \left (a +\beta \right )}{\alpha } = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.492 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+\alpha y^{2}+\beta x y+\gamma = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
57.786 |
|
|
\[ {}\left (x^{2} a +b \right ) y^{\prime }+y^{2}-2 x y+\left (1-a \right ) x^{2}-b = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
4.773 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime } = y^{2}+\left (2 \lambda x +b \right ) y+\lambda \left (\lambda -a \right ) x^{2}+\mu \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
6.681 |
|
|
\[ {}\left (x^{2} a +b x +c \right ) y^{\prime } = y^{2}+\left (x a +\mu \right ) y-\lambda ^{2} x^{2}+\lambda \left (b -\mu \right ) x +c \lambda \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
145.468 |
|
|
\[ {}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y-\lambda \left (\lambda +a_{1} -a_{2} \right ) x^{2}+\lambda \left (b_{2} -b_{1} \right ) x +\lambda c_{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
158.893 |
|
|
\[ {}\left (a_{2} x^{2}+b_{2} x +c_{2} \right ) y^{\prime } = y^{2}+\left (a_{1} x +b_{1} \right ) y+a_{0} x^{2}+b_{0} x +c_{0} \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
157.181 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
5.77 |
|
|
\[ {}\left (c_{2} x^{2}+b_{2} x +a_{2} \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b_{1} x +a_{1} \right ) y+a_{0} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
35.999 |
|
|
\[ {}x^{3} y^{\prime } = a \,x^{3} y^{2}+\left (b \,x^{2}+c \right ) y+s x \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
35.645 |
|
|
\[ {}x^{3} y^{\prime } = a \,x^{3} y^{2}+x \left (b x +c \right ) y+\alpha x +\beta \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
83.606 |
|
|
\[ {}x \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+\left (b \,x^{2}+c \right ) y+s x = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
4.635 |
|
|
\[ {}x^{2} \left (x +a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b x +c \right ) y+\alpha x +\beta = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
6.953 |
|
|
\[ {}\left (x^{2} a +b x +e \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.059 |
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\[ {}x^{2} \left (x^{2}+a \right ) \left (y^{\prime }+\lambda y^{2}\right )+x \left (b \,x^{2}+c \right ) y+s = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✗ |
7.855 |
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|
\[ {}a \left (x^{2}-1\right ) \left (y^{\prime }+\lambda y^{2}\right )+b x \left (x^{2}-1\right ) y+c \,x^{2}+d x +s = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.535 |
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