| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 4 z y^{\prime \prime }+2 \left (1-z \right ) y^{\prime }-y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+9 z^{5} y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z^{2} y^{\prime \prime }-\frac {3 z y^{\prime }}{2}+\left (1+z \right ) y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.131 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }-2 y^{\prime }+y z&=0 \end {array} \]
Series expansion around \(z=0\). |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 z y^{\prime }-2 y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z \left (1-z \right ) y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \end {array} \]
Series expansion around \(z=0\). |
[_Jacobi] |
✓ |
✓ |
✓ |
✓ |
1.511 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }+\left (2 z -3\right ) y^{\prime }+\frac {4 y}{z}&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.122 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (z^{2}+5 z +6\right ) y^{\prime \prime }+2 y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.924 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (z^{2}+5 z +7\right ) y^{\prime \prime }+2 y&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+\frac {y}{z^{3}}&=0 \end {array} \]
Series expansion around \(z=0\). |
[[_Emden, _Fowler]] |
✗ |
✗ |
✓ |
✗ |
0.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} z y^{\prime \prime }+\left (1-z \right ) y^{\prime }+\lambda y&=0 \end {array} \]
Series expansion around \(z=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
1.492 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-z^{2}+1\right ) y^{\prime \prime }-z y^{\prime }+m^{2} y&=0 \end {array} \]
Series expansion around \(z=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.120 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.354 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.789 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x +y} y^{\prime }-1&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
111.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (x -2\right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.797 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.794 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x&=3-2 x^{2} y^{\prime } \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.530 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
203.090 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (-1+x \right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.246 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{2} y-32}{-x^{2}+16}+32 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.246 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (x^{2}+1\right ) y^{\prime }+y^{2}&=-1\\ y \left (0\right )&=1\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.062 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x\\ y \left (0\right )&=2 a\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.562 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=1-\frac {\sin \left (x +y\right )}{\cos \left (x \right ) \sin \left (y\right )}\\ y \left (\frac {\pi }{4}\right )&=\frac {\pi }{4}\\ \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
103.378 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=y^{3} \sin \left (x \right ) \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.183 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-y&={\mathrm e}^{2 x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }-4 y x&=x^{7} \sin \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.431 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+2 y x&=2 x^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {2 x y}{x^{2}+1}&=4 x \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.293 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {2 x y}{x^{2}+1}&=\frac {4}{\left (x^{2}+1\right )^{2}} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.151 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right )&=4 \cos \left (x \right )^{4} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.148 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.715 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\tan \left (x \right ) y&=8 \sin \left (x \right )^{3} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.237 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} t x^{\prime }+2 x&=4 \,{\mathrm e}^{t} \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.773 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right ) \left (y \sec \left (x \right )-2\right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.754 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 1-\sin \left (x \right ) y-\cos \left (x \right ) y^{\prime }&=0 \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.888 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }-\frac {y}{x}&=2 x^{2} \ln \left (x \right ) \end {array} \]
|
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.984 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\alpha y&={\mathrm e}^{\beta x} \end {array} \]
|
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.580 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }+\frac {m}{x}&=\ln \left (x \right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.903 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \left (3 x -y\right ) y^{\prime }&=3 y \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
286.891 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (x +y\right )^{2}}{2 x^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
11.851 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} \sin \left (\frac {y}{x}\right ) \left (-y+y^{\prime } x \right )&=x \cos \left (\frac {y}{x}\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
408.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=\sqrt {16 x^{2}-y^{2}}+y \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.369 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} -y+y^{\prime } x&=\sqrt {9 x^{2}+y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
30.154 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x \left (x^{2}-y^{2}\right )-x \left (x^{2}+y^{2}\right ) y^{\prime }&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
17.883 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x +y \ln \left (x \right )&=\ln \left (y\right ) y \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.020 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.360 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 y y^{\prime } x -2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}&=0 \end {array} \]
|
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
21.731 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime }&=x^{2}+3 y x +y^{2} \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.996 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y y^{\prime }&=\sqrt {x^{2}+y^{2}}-x \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.728 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x \left (2 x +y\right ) y^{\prime }&=y \left (4 x -y\right ) \end {array} \]
|
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
29.871 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime } x&=x \tan \left (\frac {y}{x}\right )+y \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.779 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x} \end {array} \]
|
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
47.174 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-25 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.536 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+4 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-2 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=-y^{2} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.204 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{2 x} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.767 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+2 y^{\prime }+5 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.427 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +3 y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.859 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.297 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.472 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} 2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=9 x^{2} \end {array} \]
|
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x^{4} \sin \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.558 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.684 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+a^{2} y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.867 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }-y^{\prime }-6 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.209 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+6 y^{\prime }+9 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \end {array} \]
|
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.793 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.203 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
7.178 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1-y^{2}}{2 y x +2} \end {array} \]
|
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
6.468 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x}\\ y \left (1\right )&=0\\ \end {array} \]
|
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
601.388 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )} \end {array} \]
|
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
30.692 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y}\\ y \left (\pi \right )&=\frac {1}{\pi }\\ \end {array} \]
|
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.425 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\sin \left (x \right ) \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.499 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {1}{x^{{2}/{3}}} \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.123 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x \,{\mathrm e}^{x} \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.038 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x^{n} \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.033 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=x^{2} \ln \left (x \right )\\ y \left (1\right )&=2\\ \end {array} \]
|
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.886 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=\cos \left (x \right )\\ y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1\\ \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime \prime }&=6 x\\ y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=-1\\ y^{\prime \prime }\left (0\right )&=-4\\ \end {array} \]
|
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.256 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }&=x \,{\mathrm e}^{x}\\ y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=4\\ \end {array} \]
|
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.515 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime \prime }+y^{\prime }-6 y&=0 \end {array} \]
|
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-y^{\prime } x -8 y&=0 \end {array} \]
|
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.441 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{2} \ln \left (x \right ) \end {array} \]
|
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.121 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=2 y x \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.398 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y^{2}}{x^{2}+1} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.747 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} {\mathrm e}^{x +y} y^{\prime }-1&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
111.678 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {y}{x \ln \left (x \right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.076 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-\left (-1+x \right ) y^{\prime }&=0 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.056 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {2 x \left (-1+y\right )}{x^{2}+3} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y-y^{\prime } x&=3-2 x^{2} y^{\prime } \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.638 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1 \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
219.064 |
|
| \[ \begin {array}{>{\displaystyle }r @{\;} >{\displaystyle }l} y^{\prime }&=\frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (-1+x \right )} \end {array} \]
|
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.992 |
|