|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (x -2\right ) \left (x -1\right )}
\] |
[_separable] |
✓ |
2.870 |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2
\] |
[_separable] |
✓ |
1.661 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
1.684 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.834 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
2.104 |
|
|
\[
{}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )}
\] |
[_separable] |
✓ |
3.365 |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.849 |
|
|
\[
{}y^{\prime } = \frac {2 \sqrt {-1+y}}{3}
\] |
[_quadrature] |
✓ |
1.186 |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
0.953 |
|
|
\[
{}y^{\prime }+y = 4 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.270 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
0.239 |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
0.291 |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_linear] |
✓ |
0.266 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{-x^{2}+1} = 4 x
\] |
[_linear] |
✓ |
0.280 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
0.319 |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
0.316 |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
[_linear] |
✓ |
0.118 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
0.298 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
0.256 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
2.146 |
|
|
\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.335 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
0.236 |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.125 |
|
|
\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
[_linear] |
✓ |
0.162 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
[_linear] |
✓ |
0.386 |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
3.095 |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
2.087 |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.513 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.676 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.642 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.010 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.326 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.252 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.826 |
|
|
\[
{}y^{\prime } x -y = x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
1.190 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.562 |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.027 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.581 |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (y^{\prime } x -y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.718 |
|
|
\[
{}y^{\prime } x = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
61.319 |
|
|
\[
{}y^{\prime } x -y = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.748 |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.650 |
|
|
\[
{}y^{\prime } x +y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.273 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.823 |
|
|
\[
{}2 x y y^{\prime }-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}}-2 y^{2} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
3.142 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.184 |
|
|
\[
{}y y^{\prime } = \sqrt {x^{2}+y^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.811 |
|
|
\[
{}2 x \left (y+2 x \right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.758 |
|
|
\[
{}y^{\prime } x = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.414 |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {x^{2}+y^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
37.418 |
|
|
\[
{}y^{\prime } = \frac {4 y-2 x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
17.132 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.195 |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {x^{2}+y^{2}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.831 |
|
|
\[
{}y^{\prime } x -y = \sqrt {4 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
55.365 |
|
|
\[
{}y^{\prime } = \frac {x +a y}{a x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.814 |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.001 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.888 |
|
|
\[
{}y^{\prime }+\frac {y \tan \left (x \right )}{2} = 2 y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
8.814 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.097 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
[_Bernoulli] |
✓ |
2.245 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.153 |
|
|
\[
{}2 x \left (y^{\prime }+x^{2} y^{3}\right )+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.894 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
[_rational, _Bernoulli] |
✓ |
5.251 |
|
|
\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
[_Bernoulli] |
✓ |
3.114 |
|
|
\[
{}y^{\prime }+4 x y = 4 x^{3} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.333 |
|
|
\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
[_Bernoulli] |
✓ |
1.739 |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.450 |
|
|
\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
[_Bernoulli] |
✓ |
37.279 |
|
|
\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
[_separable] |
✓ |
5.062 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.969 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
[_Bernoulli] |
✓ |
4.050 |
|
|
\[
{}y^{\prime } = \left (9 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.485 |
|
|
\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
6.700 |
|
|
\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
22.097 |
|
|
\[
{}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.798 |
|
|
\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.969 |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.509 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
[_Riccati] |
✗ |
2.431 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.179 |
|
|
\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.720 |
|
|
\[
{}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.454 |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.239 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}} = \frac {1}{2 \sqrt {x +1}}
\] |
[_separable] |
✓ |
32.132 |
|
|
\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.401 |
|
|
\[
{}\cos \left (x y\right )-x y \sin \left (x y\right )-x^{2} \sin \left (x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
0.387 |
|
|
\[
{}y+3 x^{2}+y^{\prime } x = 0
\] |
[_linear] |
✓ |
0.268 |
|
|
\[
{}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.338 |
|
|
\[
{}2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.268 |
|
|
\[
{}y^{2}-2 x +2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
0.383 |
|
|
\[
{}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
0.583 |
|
|
\[
{}\frac {1}{x}-\frac {y}{x^{2}+y^{2}}+\frac {x y^{\prime }}{x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati] |
✓ |
0.444 |
|
|
\[
{}y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.341 |
|
|
\[
{}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
0.447 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.349 |
|
|
\[
{}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.335 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.076 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.090 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.504 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.043 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.083 |
|