| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +12 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
Series expansion around \(x=0\). |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\left (-1+x \right ) y\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.585 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2+x \right ) y^{\prime \prime }+2 \left (x +1\right ) y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.106 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.567 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left ({\mathrm e}^{x}-1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.249 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x -y^{\prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (2+x \right ) y^{\prime \prime }+\left (x +1\right ) y^{\prime }-4 y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +\left (\frac {1}{2}-x \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {1}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {9}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.693 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}+\frac {25}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.928 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y x&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.721 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y x&=\frac {1}{x^{3}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+y&=\frac {1}{x^{4}} \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
0.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x -2 y^{\prime }+y&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✓ |
✗ |
2.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {y}{x}&=\cos \left (x \right ) \end {array} \]
Series expansion around \(x=0\). |
[_linear] |
✗ |
✗ |
✓ |
✗ |
0.365 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=1\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.337 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x&=0 \end {array} \]
Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +p^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.812 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y-2 y^{\prime } x +\left (x^{2}+1\right ) y^{\prime \prime }&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y&=0 \end {array} \]
Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 x^{3} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.523 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y x&=\frac {1}{1-x}\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.653 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x +\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.210 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y^{\prime }}{x}-y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.864 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime } x +y^{\prime }-x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.220 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+y x&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +x^{3} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +y^{\prime } x -{\mathrm e}^{x} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime }+\left (x +1\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.085 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +x^{5} y^{\prime }+y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.826 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x \right ) y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.079 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \cos \left (x \right ) y^{\prime \prime }-\sin \left (x \right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.914 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.602 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \end {array} \]
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.846 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1-x \right ) y^{\prime \prime }-4 y^{\prime } x +5 y&=\cos \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
8.727 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }-{y^{\prime }}^{4}+y&=0 \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{5} y^{\prime \prime \prime \prime }-t^{3} y^{\prime \prime }+6 y&=0 \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }+u^{\prime }+u&=\cos \left (r +u\right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.314 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.030 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} R^{\prime \prime }&=-\frac {k}{R^{2}} \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }-\left (1-\frac {{x^{\prime }}^{2}}{3}\right ) x^{\prime }+x&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
53.600 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (y^{\prime }\right )&=x +y \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.938 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (x^{\prime }\right )+y^{3} x&=\sin \left (y \right ) \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
45.259 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}-1+y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.086 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }+y&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+20 y&=24 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-6 y^{\prime }+13 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=\tan \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.916 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (y-x \right ) y^{\prime }&=y-x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=25+y^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.517 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 x y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime }&=y^{3} \cos \left (x \right ) \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.341 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=\left (x-1\right ) \left (1-2 x\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.919 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +\left (x^{2}-y\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
16.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} p^{\prime }&=p \left (1-p\right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+4 y x&=8 x^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.150 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.623 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=12 x^{2} \end {array} \]
|
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.736 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -3 y x&=1 \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime } x -y&=2 \cos \left (x \right ) x \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +x^{2} y^{\prime }&=10 \sin \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.408 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=1 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.095 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -2 y&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.467 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime }&=2 y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.410 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y-5 y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.186 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+7 y^{\prime }-4 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime } x +2 y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 x^{2} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-7 y^{\prime } x +15 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime \prime }-3 y^{\prime \prime } x +3 y^{\prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.282 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime } x +5 y&=10 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.845 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}+2 y-3 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-1+y\right ) y^{\prime }&=1 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+6 y&=10 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.911 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=4 y \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}&=9-y^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.383 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }+\sqrt {16-y^{2}}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {y^{\prime }}^{2}-2 y^{\prime }+4 y&=4 x -1 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.540 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+3 y\\ y^{\prime }&=5 x+3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.947 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime \prime }&=4 y+{\mathrm e}^{t}\\ y^{\prime \prime }&=4 x-{\mathrm e}^{t}\\ \end {array} \]
|
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1-y^{2}} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
46.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+4 y&=5 \sin \left (t \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|