|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x^{2} y^{\prime \prime }-y^{\prime } x +y = 9 x^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.378 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y = x^{4} \sin \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
12.974 |
|
|
\[
{}y^{\prime \prime }-\left (a +b \right ) y^{\prime }+a b y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.267 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.315 |
|
|
\[
{}y^{\prime \prime }-2 a y^{\prime }+\left (a^{2}+b^{2}\right ) y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.789 |
|
|
\[
{}y^{\prime \prime }-y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.309 |
|
|
\[
{}y^{\prime \prime }+6 y^{\prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.360 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.023 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.856 |
|
|
\[
{}y^{\prime } = \frac {{\mathrm e}^{x}-\sin \left (y\right )}{x \cos \left (y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.243 |
|
|
\[
{}y^{\prime } = \frac {1-y^{2}}{2 y x +2}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.292 |
|
|
\[
{}y^{\prime } = \frac {\left (1-y \,{\mathrm e}^{y x}\right ) {\mathrm e}^{-y x}}{x}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
2.533 |
|
|
\[
{}y^{\prime } = \frac {x^{2} \left (1-y^{2}\right )+y \,{\mathrm e}^{\frac {y}{x}}}{x \left ({\mathrm e}^{\frac {y}{x}}+2 x^{2} y\right )}
\] |
[‘y=_G(x,y’)‘] |
✓ |
86.221 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y}
\] |
[_Bernoulli] |
✓ |
136.569 |
|
|
\[
{}y^{\prime } = \sin \left (x \right )
\] |
[_quadrature] |
✓ |
0.232 |
|
|
\[
{}y^{\prime } = \frac {1}{x^{{2}/{3}}}
\] |
[_quadrature] |
✓ |
0.218 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.855 |
|
|
\[
{}y^{\prime \prime } = x^{n}
\] |
[[_2nd_order, _quadrature]] |
✓ |
0.879 |
|
|
\[
{}y^{\prime } = x^{2} \ln \left (x \right )
\] |
[_quadrature] |
✓ |
1.922 |
|
|
\[
{}y^{\prime \prime } = \cos \left (x \right )
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.494 |
|
|
\[
{}y^{\prime \prime \prime } = 6 x
\] |
[[_3rd_order, _quadrature]] |
✓ |
0.137 |
|
|
\[
{}y^{\prime \prime } = x \,{\mathrm e}^{x}
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.161 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.398 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x -8 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.747 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = x^{2} \ln \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
3.418 |
|
|
\[
{}y^{\prime } = 2 y x
\] |
[_separable] |
✓ |
1.236 |
|
|
\[
{}y^{\prime } = \frac {y^{2}}{x^{2}+1}
\] |
[_separable] |
✓ |
1.400 |
|
|
\[
{}{\mathrm e}^{x +y} y^{\prime }-1 = 0
\] |
[_separable] |
✓ |
2.838 |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
3.618 |
|
|
\[
{}y-\left (x -1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.637 |
|
|
\[
{}y^{\prime } = \frac {2 x \left (-1+y\right )}{x^{2}+3}
\] |
[_separable] |
✓ |
2.942 |
|
|
\[
{}y-y^{\prime } x = 3-2 x^{2} y^{\prime }
\] |
[_separable] |
✓ |
1.410 |
|
|
\[
{}y^{\prime } = \frac {\cos \left (x -y\right )}{\sin \left (x \right ) \sin \left (y\right )}-1
\] |
[_separable] |
✓ |
4.037 |
|
|
\[
{}y^{\prime } = \frac {x \left (-1+y^{2}\right )}{2 \left (x -2\right ) \left (x -1\right )}
\] |
[_separable] |
✓ |
4.214 |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2
\] |
[_separable] |
✓ |
1.521 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
3.248 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
3.795 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+y x = a x
\] |
[_separable] |
✓ |
3.819 |
|
|
\[
{}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )}
\] |
[_separable] |
✓ |
6.465 |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.622 |
|
|
\[
{}y^{\prime } = \frac {2 \sqrt {-1+y}}{3}
\] |
[_quadrature] |
✓ |
0.692 |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
0.899 |
|
|
\[
{}y^{\prime }+y = 4 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
0.094 |
|
|
\[
{}x^{2} y^{\prime }-4 y x = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
0.105 |
|
|
\[
{}y^{\prime }+2 y x = 2 x^{3}
\] |
[_linear] |
✓ |
0.105 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{-x^{2}+1} = 4 x
\] |
[_linear] |
✓ |
0.120 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
0.115 |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
0.254 |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
[_linear] |
✓ |
0.115 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
0.139 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
0.129 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
2.080 |
|
|
\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.332 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
0.098 |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.128 |
|
|
\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
[_linear] |
✓ |
0.148 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
[_linear] |
✓ |
0.196 |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.485 |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
4.039 |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.119 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.790 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.710 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.987 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✓ |
3.069 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.009 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.786 |
|
|
\[
{}y^{\prime } x -y = x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
0.952 |
|
|
\[
{}y^{\prime } = \frac {x^{2}+y x +y^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
4.230 |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.996 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
4.224 |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (y^{\prime } x -y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
14.590 |
|
|
\[
{}y^{\prime } x = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
118.604 |
|
|
\[
{}y^{\prime } x -y = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.546 |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.193 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 y x -2 x^{2}}{x^{2}-y x +y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
25.036 |
|
|
\[
{}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
7.842 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 y x +x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
4.485 |
|
|
\[
{}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
18.062 |
|
|
\[
{}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
8.547 |
|
|
\[
{}y^{\prime } x = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.239 |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{y x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
74.454 |
|
|
\[
{}y^{\prime } = \frac {4 y-2 x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
53.289 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.306 |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.477 |
|
|
\[
{}y^{\prime } x -y = \sqrt {4 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
172.364 |
|
|
\[
{}y^{\prime } = \frac {x +a y}{a x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
15.404 |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.109 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
9.398 |
|
|
\[
{}y^{\prime }+\frac {y \tan \left (x \right )}{2} = 2 y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
22.664 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
7.964 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
[_Bernoulli] |
✓ |
3.678 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.530 |
|
|
\[
{}2 x \left (y^{\prime }+x^{2} y^{3}\right )+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
10.642 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
[_rational, _Bernoulli] |
✓ |
14.714 |
|
|
\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
[_Bernoulli] |
✓ |
9.423 |
|
|
\[
{}y^{\prime }+4 y x = 4 x^{3} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
2.226 |
|
|
\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
[_Bernoulli] |
✓ |
3.191 |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
7.806 |
|