| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.658 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {-y x -1}{4 x^{3} y-2 x^{2}} \end {array} \]
|
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
130.819 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {{y^{\prime }}^{2}}{4}-y^{\prime } x +y&=0 \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.553 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {\frac {1+y}{y^{2}}}\\ y \left (0\right )&=1\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
289.648 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1-x^{2}-y^{2}} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
2.820 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.429 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {y}+x \end {array} \]
|
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
✓ |
✗ |
48.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
18.640 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=y^{\prime } x +x^{2} {y^{\prime }}^{2} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.775 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x +y\right ) y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.072 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{x +y}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime }}{x}&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.992 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=0 \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.838 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.862 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {5 x^{2}-y x +y^{2}}{x^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
8.661 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 t +3 x+\left (2+x\right ) x^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
22.265 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{1-y}\\ y \left (0\right )&=2\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} p^{\prime }&=a p-b p^{2}\\ p \left (\operatorname {t0} \right )&=\operatorname {p0}\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
52.973 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2}+\frac {2}{x}+2 y y^{\prime } x&=0 \end {array} \]
|
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.380 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x f^{\prime }-f&=\frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \end {array} \]
|
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
14.326 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -2 y+b y^{2}&=c \,x^{4} \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x -y+y^{2}&=x^{{2}/{3}} \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
71.935 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} u^{\prime }+u^{2}&=\frac {1}{x^{{4}/{5}}} \end {array} \]
|
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.486 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }-y&=x \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
17.660 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y+2 y^{\prime }+y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 5 y^{\prime \prime }+2 y^{\prime }+4 y&=0\\ y \left (0\right )&=0\\ y^{\prime }\left (0\right )&=5\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.806 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+4 y&=1 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+4 y&=\sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y&=x {y^{\prime }}^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=1-{y^{\prime }}^{3} x \end {array} \]
|
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime }&=\frac {1}{f} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.885 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+4 y^{\prime }&=t^{2} \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.609 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (t^{2}+9\right ) y^{\prime \prime }+2 y^{\prime } t&=0\\ y \left (3\right )&=2 \pi \\ y^{\prime }\left (3\right )&={\frac {2}{3}}\\ \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.353 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-3 y^{\prime } t +5 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.011 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }+y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.368 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t^{2} y^{\prime \prime }-2 y^{\prime }&=0 \end {array} \]
|
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.896 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
16.158 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t y^{\prime \prime }-y^{\prime }+4 t^{3} y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.955 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.964 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=1 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.083 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=f \left (t \right ) \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=k \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.752 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-4 \sin \left (x -y\right )-4 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.318 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\sin \left (x -y\right )&=0 \end {array} \]
|
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=4 \sin \left (x \right )-4 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.181 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.046 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=1 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
21.688 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime \prime }&=x \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.288 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime }&=x \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.421 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{2} y^{\prime \prime }&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y y^{\prime \prime }&=\sin \left (x \right ) \end {array} \]
|
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.373 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 3 y y^{\prime \prime }+y&=5 \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
6.276 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+b y&=c \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
7.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y^{2} y^{\prime \prime }+b y^{2}&=c \end {array} \]
|
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.592 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} a y y^{\prime \prime }+b y&=0 \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=9 x+4 y\\ y^{\prime }&=-6 x-y\\ z^{\prime }&=6 x+4 y+3 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-3 y\\ y^{\prime }&=3 x+7 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.446 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x-2 y\\ y^{\prime }&=2 x+5 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=7 x+y\\ y^{\prime }&=-4 x+3 y\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=x+y\\ y^{\prime }&=y\\ z^{\prime }&=z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=2 x+y-z\\ y^{\prime }&=-x+2 z\\ z^{\prime }&=-x-2 y+4 z\\ \end {array} \]
|
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.697 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{\prime }&=4 A k \left (\frac {x}{A}\right )^{{3}/{4}}-3 k x \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
13.217 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.525 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}&=-x\\ y \left (0\right )&=3\\ \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.140 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y \left (1+\frac {a^{2} x}{\sqrt {a^{2} \left (x^{2}+1\right )}}\right )}{\sqrt {a^{2} \left (x^{2}+1\right )}} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
139.628 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+y^{2} \end {array} \]
|
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
9.185 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 \sqrt {y}\\ y \left (0\right )&=0\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
31.137 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.690 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sqrt {1-y^{2}} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.111 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2}+y^{2}-1 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
27.513 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y \left (x \sqrt {y}-1\right )\\ y \left (0\right )&=1\\ \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
4.254 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \end {array} \]
|
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
36.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y \left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y^{\prime }\left (0\right )&=0\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.350 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }+y&=0\\ y^{\prime }\left (0\right )&=0\\ y \left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.520 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y y^{\prime }&=2 x \end {array} \]
|
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
51.904 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y^{2}-x -x^{2}&=0 \end {array} \]
|
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
31.582 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.875 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -2 x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.746 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -3 x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.702 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{2}-x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.024 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{3}+2&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.180 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{4}-6&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.993 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{5}+24&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.065 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.676 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.961 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime } x -y x -x^{3}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.023 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-c x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.906 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{2}&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.687 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-a x y^{\prime }-b x y-c \,x^{3}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
4.724 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.298 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.312 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{2}-1&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.313 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-y x -x^{2}-2&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.309 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-4 y^{\prime }-y x -x^{2}-4&=0 \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.324 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{3}+1&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.902 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 y^{\prime }-y x -x^{3}-x^{2}&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.308 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-y x -x^{3}+2&=0 \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.312 |
|