| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-2 x \left (y^{3}-3 y+2\right )\\ y \left (0\right )&=3\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a \,x^{\frac {n}{1-n}}+b y^{n} \end {array} \]
|
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
6.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
6.699 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
11.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
6.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \end {array} \]
|
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-f \left (x \right ) g^{\prime }\left (x \right )&=0 \end {array} \]
|
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.400 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
13.070 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
7.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a y^{3}+\frac {b}{x^{{3}/{2}}} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
48.082 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=a \,x^{2 n +1} y^{3}+b \,x^{-n -2} \end {array} \]
|
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
55.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {{\mathrm e}^{2 \lambda x} y^{3}}{3 \lambda }+\frac {2 \lambda ^{2} {\mathrm e}^{-\lambda x}}{3} \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Abel] |
✓ |
✓ |
✓ |
✓ |
396.359 |
|