| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\cot \left (x \right ) y+\sin \left (x \right )\\ y \left (\frac {\pi }{2}\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
535.271 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x -y y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
55.643 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.922 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +x^{2}-y&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
24.109 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y \left (1-y\right )-2 y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
26.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.281 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2 x -1\right ) y+x \left (x +1\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.406 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{-1+x}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x +y\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.755 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.999 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x}\\ y \left (-1\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
41.445 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x}\\ y \left (\frac {1}{2}\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
27.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.199 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{-x^{2}+1}+\sqrt {x}\\ y \left (2\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
21.459 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
147.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}\\ y \left (-1\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
45.211 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{2}\\ y \left (1\right )&={\frac {1}{2}}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
28.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{3}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
108.970 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{3}\\ y \left (-1\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
74.206 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{3}\\ y \left (-1\right )&=-1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
67.889 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {3 x^{2}}{2 y}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
166.367 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {3 x^{2}}{2 y}\\ y \left (-1\right )&={\frac {1}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
41.698 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {3 x^{2}}{2 y}\\ y \left (-1\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {3 x^{2}}{2 y}\\ y \left (-1\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
171.233 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sqrt {y}}{x}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
39.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sqrt {y}}{x}\\ y \left (-1\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.165 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sqrt {y}}{x}\\ y \left (-1\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
40.884 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\sqrt {y}}{x}\\ y \left (1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
36.067 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x y^{{1}/{3}}\\ y \left (-1\right )&={\frac {3}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
870.605 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x y^{{1}/{3}}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
304.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x y^{{1}/{3}}\\ y \left (-1\right )&={\frac {1}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
1070.478 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x y^{{1}/{3}}\\ y \left (-1\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
157.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3 x y^{{1}/{3}}\\ y \left (-1\right )&=-1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
594.827 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
36.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.816 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {\left (y+2\right ) \left (-1+y\right )}\\ y \left (0\right )&=-3\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
19.201 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{y-x}\\ y \left (1\right )&=2\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
304.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{y-x}\\ y \left (1\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
108.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{y-x}\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
302.674 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{y-x}\\ y \left (1\right )&=-1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
193.758 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y x}{x^{2}+y^{2}}\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
272.428 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y x}{x^{2}+y^{2}}\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
437.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y x}{x^{2}+y^{2}}\\ y \left (0\right )&=-1\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
402.051 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \sqrt {1-y^{2}}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \sqrt {1-y^{2}}\\ y \left (0\right )&={\frac {9}{10}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
226.061 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \sqrt {1-y^{2}}\\ y \left (0\right )&={\frac {1}{2}}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
78.868 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x \sqrt {1-y^{2}}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
32.125 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
237.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
250.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}\\ y \left (0\right )&=-1\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
194.805 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}\\ y \left (1\right )&=-{\frac {1}{5}}\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
73.594 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2}\\ y \left (1\right )&=-{\frac {1}{4}}\\ \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
65.550 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y^{\prime \prime }-2 y^{\prime }+4 y&=x\\ y \left (-1\right )&=2\\ y^{\prime }\left (-1\right )&=3\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.552 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x y^{\prime \prime \prime }+y^{\prime } x&=4\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ y^{\prime \prime }\left (1\right )&=-1\\ \end {array} \]
|
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.865 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2}\\ y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.170 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x -3\right ) y^{\prime \prime }+3 y^{\prime }&=x^{2}\\ y \left (5\right )&=0\\ y^{\prime }\left (5\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.546 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sqrt {1-x}\, y^{\prime \prime }-4 y&=\sin \left (x \right )\\ y \left (-2\right )&=3\\ y^{\prime }\left (-2\right )&=-1\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
7.135 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}-4\right ) y^{\prime \prime }+y \ln \left (x \right )&=x \,{\mathrm e}^{x}\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=2\\ \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
5.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
12.663 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
10.595 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end {array} \]
|
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
11.417 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
14.963 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime }&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x +y&=0\\ y \left (1\right )&=2\\ y^{\prime }\left (1\right )&=-1\\ \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y&=31\\ y \left (0\right )&=-9\\ y^{\prime }\left (0\right )&=6\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
11.901 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=27 x +18\\ y \left (0\right )&=23\\ y^{\prime }\left (0\right )&=21\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -4 y&=-3 x -\frac {3}{x}\\ y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=-6\\ \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
170.422 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+4 y^{\prime }-3 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.281 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -4 y+6 y^{\prime }-4 y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.144 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.092 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.160 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-8 y^{\prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.153 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 36 y^{\prime \prime \prime \prime }-12 y^{\prime \prime \prime }-11 y^{\prime \prime }+2 y^{\prime }+y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+35 y^{\prime \prime }+16 y^{\prime }-52 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (8\right )}+8 y^{\prime \prime \prime \prime }+16 y&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.193 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\alpha y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
11.871 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+\left (-3-4 i\right ) y^{\prime \prime }+\left (-4+12 i\right ) y^{\prime }+12 y&=0 \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+\left (-3-i\right ) y^{\prime \prime \prime }+\left (4+3 i\right ) y^{\prime \prime }&=0 \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-i y&=0\\ y \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.466 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-6 y^{\prime \prime \prime }+13 y^{\prime \prime }-12 y^{\prime }+4 y&=2 \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x} \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.606 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.936 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3+\cos \left (2 x \right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime }&=6 x -20-120 \,{\mathrm e}^{x} x^{2} \end {array} \]
|
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.387 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-6 y^{\prime \prime }+21 y^{\prime }-26 y&=36 \,{\mathrm e}^{2 x} \sin \left (3 x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \end {array} \]
|
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\left (6\right )}-12 y^{\left (5\right )}+63 y^{\prime \prime \prime \prime }-18 y^{\prime \prime \prime }+315 y^{\prime \prime }-300 y^{\prime }+125 y&={\mathrm e}^{x} \left (48 \cos \left (x \right )+96 \sin \left (x \right )\right ) \end {array} \]
|
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.503 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=5\\ y^{\prime \prime }\left (0\right )&=-1\\ \end {array} \]
|
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.479 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime }-y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=-3\\ y^{\prime \prime \prime }\left (0\right )&=3\\ \end {array} \]
|
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.471 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=2 \,{\mathrm e}^{x}\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=-3\\ \end {array} \]
|
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.500 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 x +4\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=0\\ y^{\prime \prime }\left (0\right )&=1\\ y^{\prime \prime \prime }\left (0\right )&=1\\ \end {array} \]
|
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&=0 \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.655 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=0 \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&=4 \end {array} \]
Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.910 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=2 \sin \left (3 x \right ) \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.968 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+9 y&=2 \sin \left (3 x \right ) \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.979 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=x \,{\mathrm e}^{x}-3 x^{2} \end {array} \]
Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+y^{\prime \prime }&=x \,{\mathrm e}^{x}-3 x^{2} \end {array} \]
Using Laplace transform method. |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.530 |
|