| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=7\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.976 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+36 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=7\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.139 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.570 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.052 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +25 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.824 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=72 x^{5} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.351 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=8 x^{{4}/{3}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.172 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+4 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.003 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +\frac {5 y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
6.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime } t +{\mathrm e}^{-t^{2}} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.659 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.685 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t +\frac {y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 t^{2} y^{\prime \prime }-8 y^{\prime } t +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+5 y^{\prime } t +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.744 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
12.559 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
12.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=2 x^{2}+2 \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.701 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{{5}/{2}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.097 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{4} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
14.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.929 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-5 y^{\prime } t +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.285 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.900 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.960 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.881 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+2 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.944 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t -1\right )^{2} y^{\prime \prime }-2 \left (t -1\right ) y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-2+t \right )^{2} y^{\prime \prime }+5 \left (-2+t \right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.348 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +4 y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.995 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.930 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.887 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=1-x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.327 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y&=\left (-1+x \right ) \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
49.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+3 \left (x +1\right ) y^{\prime }+y&=x^{2} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.905 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.581 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.082 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=9 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.545 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=8 x \ln \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=4 \,{\mathrm e}^{2 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\frac {x^{2}}{\ln \left (x \right )} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.566 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{2}+2 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.821 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
29.827 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.405 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✓ |
✗ |
2.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y \sin \left (x \right )^{2}-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{2 x} y-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a y+y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.740 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.835 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.834 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=a \,x^{2} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \left (x +3\right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.315 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=3 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.778 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.551 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{5} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.395 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.228 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=a -x +x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
9.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.347 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=5 x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x +1\right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{2} \left (x^{2}-1\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 13 y+5 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
7.487 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 x^{2} y-x^{2} y^{\prime }+x^{2} y^{\prime \prime }&=1+x +2 x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.206 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{2} y+y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.419 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.866 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-\left (2+x \right ) y^{\prime }+\left (2+x \right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.557 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
|
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.097 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 8 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
|
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.786 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y a \,x^{3}-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (x +1\right )^{3} y+y^{\prime } x +x^{2} \left (x +1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a^{2} y+2 x^{3} y^{\prime }+x^{4} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.662 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.822 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.912 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+\left (1-2 x \right ) \left (1-x \right ) x y^{\prime }+\left (1-x \right )^{2} x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-2 \left (a -x \right )^{3} y^{\prime }+\left (a -x \right )^{4} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+x^{3} \left (3 x^{2}+a \right ) y^{\prime }+x^{6} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-a^{2}+4 b \right ) y+12 x^{5} y^{\prime }+4 x^{6} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.320 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-a \right )^{2} y+a \,x^{2 a -1} y^{\prime }+x^{2 a} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.565 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.223 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.091 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2} {\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=8 x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x -\frac {1}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=2 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=2 x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\frac {y^{\prime }}{2}+2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.980 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.782 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.854 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.134 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x +x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.119 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\ln \left (x \right )^{2}-\ln \left (x^{2}\right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.923 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y&=\ln \left (x +1\right )^{2}+x -1 \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.644 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{8} y^{\prime \prime }+4 x^{7} y^{\prime }+y&=\frac {1}{x^{3}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.691 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -3 y^{\prime }+\frac {3 y}{x}&=2+x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
10.117 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.753 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{2}+2 x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\frac {y}{4}&=-\frac {x^{2}}{2}+\frac {1}{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.372 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -1\right )^{2} y^{\prime \prime }+\left (9 x -3\right ) y^{\prime }-9 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.041 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +\alpha ^{2} y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.732 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 \pi y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
14.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.259 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
19.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {2}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
17.074 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.053 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.830 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
6.200 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{x}-x^{2} y-x^{3}-\frac {1}{x}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.483 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+x^{3} y^{\prime }-4 x^{2} y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.385 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.952 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.245 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.008 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -c^{2} y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.448 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=2 x^{3}-x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.664 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=8 x^{3} \sin \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.750 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.708 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.078 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+{\mathrm e}^{2 x} y-{\mathrm e}^{3 x}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.482 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \sin \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.381 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.840 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-y a \,x^{3}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x +2 y^{\prime }-y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2}&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +a y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.741 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right )&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
16.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y-x^{3} \sin \left (x \right )&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.763 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
8.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.709 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 50 x \left (-1+x \right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y&=0 \end {array} \]
|
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.646 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime }+y a \,x^{3}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {2 y^{\prime }}{x}-\frac {a^{2} y}{x^{4}} \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.889 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}+1}-\frac {y}{\left (x^{2}+1\right )^{2}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-a \,x^{2 a -1} x^{-2 a} y^{\prime }-b^{2} x^{-2 a} y \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {y^{\prime }}{x \ln \left (x \right )}+\ln \left (x \right )^{2} y \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.106 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\left (\sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }}{\sin \left (x \right )}-y \sin \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.579 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=-\frac {\cos \left (x \right ) y^{\prime }}{\sin \left (x \right )}+\frac {y}{\sin \left (x \right )^{2}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
58.350 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\frac {y^{\prime }}{2}+a y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +n y^{\prime }+b \,x^{1-2 n} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.722 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n^{2} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 a x +x^{2}+b \right ) y^{\prime \prime }+\left (a +x \right ) y^{\prime }-m^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+2 b x +c \right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+d y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \,x^{2}-c \right ) y^{\prime }+\lambda \,x^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
12.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
✗ |
126.127 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (a \,x^{2}+b x +c \right ) y^{\prime \prime }+\left (a \left (2-k \right ) x^{2}+b \left (1-k \right ) x -c k \right ) y^{\prime }+\lambda \,x^{1+k} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
✗ |
11.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a \,x^{2}+b \right )^{2} y^{\prime \prime }+2 a x \left (a \,x^{2}+b \right ) y^{\prime }+c y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2 n}+a \right ) y^{\prime \prime }+\left (x^{2 n}+a -a n \right ) y^{\prime }-b^{2} x^{2 n -1} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a y^{\prime }+b \,{\mathrm e}^{2 a x} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2} {\mathrm e}^{2 \lambda x}+b \right ) y^{\prime \prime }-b \lambda y^{\prime }-a^{2} \lambda ^{2} k^{2} {\mathrm e}^{2 \lambda x} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (a \,{\mathrm e}^{\lambda x}+b \right ) y^{\prime \prime }+a \lambda \,{\mathrm e}^{\lambda x} y^{\prime }+c y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
18.889 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.651 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+{\mathrm e}^{2 x} y&={\mathrm e}^{4 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.991 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.979 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right )^{2} y^{\prime \prime }+4 \left (-1+x \right ) y^{\prime }+2 y&=\cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.626 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+3 t x^{\prime }+x&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.799 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }+4 x^{\prime }+\frac {2 x}{t}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-7 t x^{\prime }+16 x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.953 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-3 t x^{\prime }+3 x&=4 t^{7} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-6 y^{\prime } x +10 y&=3 x^{4}+6 x^{3} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.573 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }-4 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.690 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.114 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.853 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=4 x -6 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=2 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.410 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=4 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.278 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=2 x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.186 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=4 \sin \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.113 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -3\right )^{2} y^{\prime \prime }-6 \left (2 x -3\right ) y^{\prime }+12 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime \prime }-2 x^{\prime }+9 t^{5} x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.895 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+3 t x^{\prime }+3 x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.839 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+t x^{\prime }+x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.332 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0\\ y \left (1\right )&=0\\ y \left ({\mathrm e}^{\pi }\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }+\frac {\lambda y}{x}&=0\\ y \left (1\right )&=0\\ y^{\prime }\left ({\mathrm e}^{\pi }\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.981 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }+\frac {\lambda y}{x^{2}+1}&=0\\ y \left (0\right )&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\frac {6 y^{\prime } x}{\left (3 x^{2}+1\right )^{2}}+\frac {y^{\prime \prime }}{3 x^{2}+1}+\lambda \left (3 x^{2}+1\right ) y&=0\\ y \left (0\right )&=0\\ y \left (\pi \right )&=0\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=2 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=2 \cos \left (\ln \left (x +1\right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.189 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=\cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
46.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=t^{7} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.994 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.010 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
10.453 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=-1\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=5\\ y^{\prime }\left (1\right )&=3\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.719 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
11.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
9.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
10.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -25 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
9.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y&=0\\ y \left (1\right )&={\frac {1}{2}}\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
11.591 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.089 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=22 x +24 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
10.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.999 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.885 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=4 x^{2}+2 x +3 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.190 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=\frac {5}{x^{3}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.514 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {50}{x^{3}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=85 \cos \left (2 \ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=4 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=\frac {10}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=6 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=64 x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.455 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 \sqrt {x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
12.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=12 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.106 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.449 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=x^{3} {\mathrm e}^{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
13.418 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.568 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 16 y-7 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
9.908 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.847 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
9.426 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=3 \sqrt {x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=6 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=\frac {1}{x^{2}+1} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.325 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (x +1\right )^{2}} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.159 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
11.697 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-12 y^{\prime } x +42 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.300 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}}&=\frac {1}{t} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.613 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.100 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.994 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=\ln \left (t \right ) \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=t \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.982 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.370 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.889 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.183 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.075 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\frac {1}{x^{5}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.377 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=8 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.616 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.015 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.880 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.400 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.422 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (-1\right )&=0\\ y^{\prime }\left (-1\right )&=1\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.948 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-5 y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.954 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.529 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +25 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.146 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=8 x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.946 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.666 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.598 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=x \left (6-\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.992 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=2 \ln \left (x \right )^{2}+12 x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.196 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x +2 y^{\prime }+y&=1\\ y \left (\infty \right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.879 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.633 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.527 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +\frac {5 y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.853 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.581 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
7.357 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.938 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0\\ y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=3\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
7.665 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.756 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}+2 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
9.005 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=4 t^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +5 y&=t \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=2 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }&=y \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.103 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.356 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.874 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.983 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y x&=1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+10 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.589 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.835 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.689 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (x^{2}-1\right ) y^{\prime }+x^{3} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.334 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-6 t x^{\prime }+12 x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.992 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }-2 t x^{\prime }+2 x&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.784 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.130 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} v^{\prime \prime }+\frac {2 x v^{\prime }}{x^{2}+1}+\frac {v}{\left (x^{2}+1\right )^{2}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.025 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\frac {2 y}{x^{2}}&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.987 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.234 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.236 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.042 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.353 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.239 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.323 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+4 \csc \left (x \right )^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.437 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.959 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.510 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.175 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.502 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +5 y&=\frac {1}{x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.213 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=2 \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.068 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +5 y&=x^{5} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.222 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=x^{m} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{m} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&={\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.230 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
53.642 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5+2 x \right ) y^{\prime }+8 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.105 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=2 x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.765 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +m^{2} y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.420 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-y \sin \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.831 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.876 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 y \sin \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.382 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=8 x^{3} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.361 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x&=m^{2} y \end {array} \]
|
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.003 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.932 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=2 x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.800 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=\frac {1}{\left (1-x \right )^{2}} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-4 \left (a +x \right ) y^{\prime }+\left (a +x \right )^{2} y^{\prime \prime }&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.414 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.918 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+\frac {\csc \left (x \right )^{2} y}{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{6} y^{\prime \prime }+3 x^{5} y^{\prime }+a^{2} y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=8 x^{3} \sin \left (x^{2}\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.022 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }+\sin \left (x \right ) y^{\prime }-2 \cos \left (x \right )^{3} y&=2 \cos \left (x \right )^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y&=4 \cos \left (\ln \left (x +1\right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.392 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&={\mathrm e}^{x} x^{2} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.890 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.541 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=x^{2}+x \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.432 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=2 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+a t x^{\prime }+x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.345 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} x^{\prime \prime }+t x^{\prime }+x&=t \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.872 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime }-\frac {4 y}{x}&=x^{3}+x \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.814 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x^{3} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right )^{2} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }-k^{2} \cos \left (x \right )^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+7 y^{\prime } x +8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.505 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
8.878 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
10.495 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.847 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=x \,{\mathrm e}^{-x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.590 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.059 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.932 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=x^{2}+16 \ln \left (x \right )^{2} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} i^{\prime \prime }+2 i^{\prime } t +i&=t \ln \left (t \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.534 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=\sqrt {x}+\frac {1}{\sqrt {x}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.506 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.069 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.377 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x -2 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }+\left (3 \sin \left (x \right )^{2}-\cos \left (x \right )\right ) y^{\prime }+2 \sin \left (x \right )^{3} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.788 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+y&=\frac {1}{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.941 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=24 x +24 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.975 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.044 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
12.270 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x^{2} y^{\prime \prime }+4 y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right )^{2} y^{\prime \prime }+5 \left (-1+x \right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.291 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +3\right )^{2} y^{\prime \prime }+3 \left (x +3\right ) y^{\prime }+5 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }+y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.461 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.009 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (-1\right )&=1\\ y^{\prime }\left (-1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
12.608 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\frac {5 y^{\prime }}{x}+\frac {5 y}{x^{2}}&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime } x -4 y^{\prime }+\frac {5 y}{x}&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
3.366 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2+x \right ) y^{\prime \prime }-y^{\prime }+\frac {y}{2+x}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.412 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {5 y^{\prime }}{-1+x}+\frac {4 y}{\left (-1+x \right )^{2}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }+\frac {3 y^{\prime }}{x -3}+\frac {3 y}{\left (x -3\right )^{2}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.913 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=\tan \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
23.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=\sqrt {x} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
13.629 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\ln \left (x \right ) \left (\frac {1}{x^{3}}+\frac {1}{x^{5}}\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.792 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=6 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.396 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t^{2} y^{\prime \prime }+2 y^{\prime } t +y&={\mathrm e}^{2 t} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
13.511 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -y&=\sqrt {t} \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
7.870 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=t^{5} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
5.228 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t^{2} y^{\prime \prime }-5 y^{\prime } t +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 t^{2} y^{\prime \prime }+3 y^{\prime } t +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +9 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.718 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.985 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.915 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime } t +2 y&=t^{4} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.977 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-y^{\prime } t +y&=t \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.783 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\tan \left (t \right ) y^{\prime }-\sec \left (t \right )^{2} y&=t \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
262.014 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=4 t^{5} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.880 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=\sec \left (\ln \left (x \right )\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.335 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=\ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.427 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.269 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.737 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.549 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.247 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y+1&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.015 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=x \,{\mathrm e}^{2 x}-1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.390 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.871 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
5.039 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 \left (x^{2}+x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }-y&=2 \sqrt {x^{2}+x} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime } x +2 y^{\prime }+y&=1\\ y \left (\infty \right )&=1\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
15.142 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\frac {y^{\prime }}{2}+\frac {y}{4}&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.152 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.702 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+3 y^{\prime } x +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+6 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.050 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-5 y^{\prime } x +58 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.931 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+25 y^{\prime } x +144 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.925 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-11 y^{\prime } x +35 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0\\ y \left (1\right )&=4\\ y^{\prime }\left (1\right )&=5\\ \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+25 y^{\prime } x +144 y&=0\\ y \left (1\right )&=-4\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.286 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=8 x^{3} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.600 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=10 x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.734 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=3 x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.436 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.823 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a x +1\right )^{2} y^{\prime \prime }+a \left (a x +1\right ) y^{\prime }+b^{2} y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=4 y \end {array} \]
|
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.715 |
|