| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
3.222 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (1-a \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
3.130 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+\left (1+a \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
2.881 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+2 n y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} b y+a y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} b x y+a y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.796 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
3.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} b \,x^{k} y+a y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.187 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.984 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n y+\left (1-x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
3.340 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} n y+\left (1+k -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
27.156 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \left (1-x \right ) y-\left (x +1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-\left (-x +2\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.863 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} b y+\left (a +x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.781 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a y+\left (c -x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
3.814 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.224 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=x^{2}-x -1 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.299 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.998 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a b x +a n +b m \right ) y+\left (m +n +\left (a +b \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x -\left (-x^{2}+4\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.742 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.136 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.267 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=4 x^{3} {\mathrm e}^{-x^{2}} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.352 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.234 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a \,x^{2} \left (a \,x^{3}+1\right ) y-\left (-2 a \,x^{3}+1\right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.362 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.273 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 \left (-x +2\right ) y-\left (9-4 x \right ) y^{\prime }+\left (3-x \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.438 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -2 y^{\prime }+\left (a -x \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.452 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (a +x \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
15.510 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_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 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b x +a \right ) y+y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y x -\left (2 x^{2}+1\right ) y^{\prime }+2 y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-\left (2+x \right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3-x \right ) y-\left (-3 x +4\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.965 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+4 y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-2 y^{\prime }+4 y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+4 \coth \left (x \right ) y^{\prime }+4 y^{\prime \prime } x&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
✗ |
33.933 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b x +a \right ) y+8 y^{\prime }+16 y^{\prime \prime } x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.080 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
18.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x +\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.286 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }&=b x +a \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }&=2 y \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }&=6 y \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.182 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }&=12 y \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=x^{4} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.342 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (a^{2} x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.058 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-a^{2} x^{2}+6\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (n \left (n -1\right )-a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.494 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.166 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (a \left (-1+a \right )-b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -b \left (b \,x^{2}+a \right ) y+a y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \end {array} \]
|
[[_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 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -a^{2} y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.279 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.244 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (p^{2}-x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
0.542 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (p^{2}+x^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_Bessel, _modified]] |
✓ |
✓ |
✓ |
✓ |
2.019 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (i x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-a^{2} x^{2}+p^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (c \,x^{2}+b x +a \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
28.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (-x^{4}+4 a \,x^{2}+n^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
36.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
29.255 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (m +1\right ) x^{m} a \left (m \right ) y+y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✓ |
27.138 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+\left (a +x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \end {array} \]
|
[[_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 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.049 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=-x +2 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (a^{2} x^{2}+2\right ) y-2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.539 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (b \,x^{2}+a \right ) y+2 y^{\prime } x +x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.017 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
8.706 |
|