| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x -2 \,{\mathrm e}^{y x} \sin \left (2 x \right )+{\mathrm e}^{y x} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{y x} x \cos \left (2 x \right )\right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
10.641 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.316 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \ln \left (x \right )+y x +\left (y \ln \left (x \right )+y x \right ) y^{\prime }&=0 \end {array} \]
|
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✗ |
✗ |
✗ |
69.714 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.990 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x -y+\left (-x +2 y\right ) y^{\prime }&=0\\ y \left (1\right )&=3\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
61.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime }&=0\\ y \left (1\right )&=0\\ \end {array} \]
|
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
143.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
7.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
356.102 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-1+{\mathrm e}^{2 x}+y \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.695 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
11.855 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+\left (-{\mathrm e}^{-2 y}+2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.331 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime }&=0 \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
10.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
506.752 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y x +y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
148.490 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{3}-2 y}{x} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
9.493 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.967 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 x +y}{3-x +3 y^{2}}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
8.413 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=3-6 x +y-2 y x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.668 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-1-2 y x -y^{2}}{x^{2}+2 y x} \end {array} \]
|
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
147.389 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y x +y^{\prime } x&=1-y\\ y \left (1\right )&=0\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {4 x^{3}+1}{y \left (2+3 y\right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +2 y&=\frac {\sin \left (x \right )}{x}\\ y \left (2\right )&=1\\ \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
8.607 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{y-2}&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
310.694 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime }&=0 \end {array} \]
|
[_exact] |
✓ |
✓ |
✓ |
✗ |
6.214 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+y&=\frac {1}{{\mathrm e}^{x}+1} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.423 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1+2 x +y^{2}+2 x y^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.252 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x +y+\left (x +2 y\right ) y^{\prime }&=0\\ y \left (2\right )&=3\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
47.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=y-{\mathrm e}^{x} y \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.287 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \end {array} \]
|
[NONE] |
✓ |
✓ |
✓ |
✗ |
46.447 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{2 x}+3 y \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.440 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y+y^{\prime }&={\mathrm e}^{-x^{2}-2 x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.907 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.790 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&={\mathrm e}^{x +y} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
195.171 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {-4+6 y x +2 y^{2}}{3 x^{2}+4 y x +3 y^{2}}+y^{\prime }&=0 \end {array} \]
|
[_rational] |
✓ |
✓ |
✓ |
✗ |
368.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{2}-1}{1+y^{2}}\\ y \left (-1\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.932 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (1+t \right ) y+y^{\prime } t&={\mathrm e}^{2 t} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.475 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
464.435 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime }&=0 \end {array} \]
|
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.596 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&={\mathrm e}^{\frac {y}{x}} x +y \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
542.486 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x}{x^{2}+y+y^{3}} \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 t +2 y&=-y^{\prime } t \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.631 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x +y}{x -y} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
26.325 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
44.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 y x}\\ y \left (1\right )&=-2\\ \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
76.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{\prime \prime }-y^{\prime }-y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }-3 y^{\prime }+y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
183.757 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.311 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y^{\prime }+9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.599 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+3 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 6 y^{\prime \prime }-5 y^{\prime }+y&=0\\ y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
4.292 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+3 y^{\prime }&=0\\ y \left (0\right )&=-2\\ y^{\prime }\left (0\right )&=3\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
6.717 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+3 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+y^{\prime }-4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.917 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+8 y^{\prime }-9 y&=0\\ y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-y&=0\\ y \left (-2\right )&=1\\ y^{\prime }\left (-2\right )&=-1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
12.597 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y&=0\\ y \left (0\right )&={\frac {5}{4}}\\ y^{\prime }\left (0\right )&=-{\frac {3}{4}}\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
7.707 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }-3 y^{\prime }+y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&={\frac {1}{2}}\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.584 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-2 y&=0\\ y \left (0\right )&=\alpha \\ y^{\prime }\left (0\right )&=2\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.524 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }-y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=\beta \\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
19.184 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y^{\prime \prime }+3 y^{\prime }-2 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-\beta \\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+5 y^{\prime }+6 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=\beta \\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.649 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.997 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+6 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.488 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }-8 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.272 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.327 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+13 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.402 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 y^{\prime \prime }+9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.063 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 9 y^{\prime \prime }+9 y^{\prime }-4 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.407 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4}&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.951 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
11.339 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y^{\prime }+5 y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.700 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }+5 y&=0\\ y \left (\frac {\pi }{2}\right )&=0\\ y^{\prime }\left (\frac {\pi }{2}\right )&=2\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y&=0\\ y \left (\frac {\pi }{3}\right )&=2\\ y^{\prime }\left (\frac {\pi }{3}\right )&=-4\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
46.971 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+\frac {5 y}{4}&=0\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+2 y&=0\\ y \left (\frac {\pi }{4}\right )&=2\\ y^{\prime }\left (\frac {\pi }{4}\right )&=-2\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.639 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime \prime }-u^{\prime }+2 u&=0\\ u \left (0\right )&=2\\ u^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.218 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 u^{\prime \prime }+2 u^{\prime }+7 u&=0\\ u \left (0\right )&=2\\ u^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+6 y&=0\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=\alpha \\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.999 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y&=0\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.624 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+y^{\prime } t +y&=0 \end {array} \]
|
[[_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 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t -6 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-4 y^{\prime } t +6 y&=0 \end {array} \]
|
[[_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 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+3 y^{\prime } t -3 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.434 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }+7 y^{\prime } t +10 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.277 |
|