|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \frac {x \left (y^{2}-1\right )}{2 \left (-2+x \right ) \left (x -1\right )}
\] |
[_separable] |
✓ |
2.576 |
|
|
\[
{}y^{\prime } = \frac {x^{2} y-32}{-x^{2}+16}+2
\] |
[_separable] |
✓ |
1.401 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }-y+c = 0
\] |
[_separable] |
✓ |
1.732 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.399 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = a x
\] |
[_separable] |
✓ |
2.130 |
|
|
\[
{}y^{\prime } = 1-\frac {\sin \left (x +y\right )}{\sin \left (y\right ) \cos \left (x \right )}
\] |
[_separable] |
✓ |
3.208 |
|
|
\[
{}y^{\prime } = y^{3} \sin \left (x \right )
\] |
[_separable] |
✓ |
2.553 |
|
|
\[
{}y^{\prime } = \frac {2 \sqrt {y-1}}{3}
\] |
[_quadrature] |
✓ |
1.246 |
|
|
\[
{}m v^{\prime } = m g -k v^{2}
\] |
[_quadrature] |
✓ |
0.960 |
|
|
\[
{}y^{\prime }+y = 4 \,{\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.174 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
0.155 |
|
|
\[
{}x^{2} y^{\prime }-4 x y = x^{7} \sin \left (x \right )
\] |
[_linear] |
✓ |
0.197 |
|
|
\[
{}y^{\prime }+2 x y = 2 x^{3}
\] |
[_linear] |
✓ |
0.185 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{-x^{2}+1} = 4 x
\] |
[_linear] |
✓ |
0.189 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = \frac {4}{\left (x^{2}+1\right )^{2}}
\] |
[_linear] |
✓ |
0.223 |
|
|
\[
{}2 \cos \left (x \right )^{2} y^{\prime }+y \sin \left (2 x \right ) = 4 \cos \left (x \right )^{4}
\] |
[_linear] |
✓ |
0.225 |
|
|
\[
{}y^{\prime }+\frac {y}{x \ln \left (x \right )} = 9 x^{2}
\] |
[_linear] |
✓ |
0.164 |
|
|
\[
{}y^{\prime }-y \tan \left (x \right ) = 8 \sin \left (x \right )^{3}
\] |
[_linear] |
✓ |
0.214 |
|
|
\[
{}x^{\prime } t +2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
0.174 |
|
|
\[
{}y^{\prime } = \sin \left (x \right ) \left (y \sec \left (x \right )-2\right )
\] |
[_linear] |
✓ |
1.978 |
|
|
\[
{}1-y \sin \left (x \right )-\cos \left (x \right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
0.241 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = 2 x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
0.162 |
|
|
\[
{}y^{\prime }+\alpha y = {\mathrm e}^{\beta x}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.126 |
|
|
\[
{}y^{\prime }+\frac {m y}{x} = \ln \left (x \right )
\] |
[_linear] |
✓ |
0.160 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 4 x
\] |
[_linear] |
✓ |
0.302 |
|
|
\[
{}y^{\prime } \sin \left (x \right )-y \cos \left (x \right ) = \sin \left (2 x \right )
\] |
[_linear] |
✓ |
2.872 |
|
|
\[
{}x^{\prime }+\frac {2 x}{4-t} = 5
\] |
[_linear] |
✓ |
1.767 |
|
|
\[
{}y-{\mathrm e}^{x}+y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.245 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1 & x \le 1 \\ 0 & 1<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.570 |
|
|
\[
{}y^{\prime }-2 y = \left \{\begin {array}{cc} 1-x & x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.549 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x} = 9 x
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.251 |
|
|
\[
{}y^{\prime }+\frac {y}{x} = \cos \left (x \right )
\] |
[_linear] |
✓ |
1.180 |
|
|
\[
{}y^{\prime }+y = {\mathrm e}^{-2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.023 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = 2 \cos \left (x \right )
\] |
[_linear] |
✓ |
1.661 |
|
|
\[
{}x y^{\prime }-y = x^{2} \ln \left (x \right )
\] |
[_linear] |
✓ |
0.969 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+x y+x^{2}}{x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.103 |
|
|
\[
{}\left (3 x -y\right ) y^{\prime } = 3 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.464 |
|
|
\[
{}y^{\prime } = \frac {\left (x +y\right )^{2}}{2 x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.133 |
|
|
\[
{}\sin \left (\frac {y}{x}\right ) \left (x y^{\prime }-y\right ) = x \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.121 |
|
|
\[
{}x y^{\prime } = \sqrt {16 x^{2}-y^{2}}+y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
75.094 |
|
|
\[
{}x y^{\prime }-y = \sqrt {9 x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.852 |
|
|
\[
{}y \left (x^{2}-y^{2}\right )-x \left (x^{2}-y^{2}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.276 |
|
|
\[
{}x y^{\prime }+y \ln \left (x \right ) = y \ln \left (y\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.076 |
|
|
\[
{}y^{\prime } = \frac {y^{2}+2 x y-2 x^{2}}{x^{2}-x y+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.478 |
|
|
\[
{}2 x y y^{\prime }-2 y^{2}-x^{2} {\mathrm e}^{-\frac {y^{2}}{x^{2}}} = 0
\] |
[[_homogeneous, ‘class A‘]] |
✓ |
2.797 |
|
|
\[
{}x^{2} y^{\prime } = y^{2}+3 x y+x^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.709 |
|
|
\[
{}y y^{\prime } = \sqrt {y^{2}+x^{2}}-x
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.378 |
|
|
\[
{}2 x \left (2 x +y\right ) y^{\prime } = y \left (4 x -y\right )
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.288 |
|
|
\[
{}x y^{\prime } = x \tan \left (\frac {y}{x}\right )+y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.804 |
|
|
\[
{}y^{\prime } = \frac {x \sqrt {y^{2}+x^{2}}+y^{2}}{x y}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
35.864 |
|
|
\[
{}y^{\prime } = \frac {4 y-2 x}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.458 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{4 y+x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.830 |
|
|
\[
{}y^{\prime } = \frac {y-\sqrt {y^{2}+x^{2}}}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.411 |
|
|
\[
{}x y^{\prime }-y = \sqrt {4 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
65.329 |
|
|
\[
{}y^{\prime } = \frac {x +a y}{a x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.346 |
|
|
\[
{}y^{\prime } = \frac {x +\frac {y}{2}}{\frac {x}{2}-y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.678 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = \frac {4 x^{2} \cos \left (x \right )}{y}
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.615 |
|
|
\[
{}y^{\prime }+\frac {y \tan \left (x \right )}{2} = 2 y^{3} \sin \left (x \right )
\] |
[_Bernoulli] |
✓ |
8.451 |
|
|
\[
{}y^{\prime }-\frac {3 y}{2 x} = 6 y^{{1}/{3}} x^{2} \ln \left (x \right )
\] |
[_Bernoulli] |
✓ |
2.043 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 \sqrt {x^{2}+1}\, \sqrt {y}
\] |
[_Bernoulli] |
✓ |
2.152 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 6 y^{2} x^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.849 |
|
|
\[
{}2 x \left (y^{\prime }+y^{3} x^{2}\right )+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.786 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right ) = 2 \left (b -a \right ) y
\] |
[_rational, _Bernoulli] |
✓ |
5.333 |
|
|
\[
{}y^{\prime }+\frac {6 y}{x} = \frac {3 y^{{2}/{3}} \cos \left (x \right )}{x}
\] |
[_Bernoulli] |
✓ |
3.052 |
|
|
\[
{}y^{\prime }+4 x y = 4 x^{3} \sqrt {y}
\] |
[_Bernoulli] |
✓ |
1.354 |
|
|
\[
{}y^{\prime }-\frac {y}{2 x \ln \left (x \right )} = 2 x y^{3}
\] |
[_Bernoulli] |
✓ |
1.721 |
|
|
\[
{}y^{\prime }-\frac {y}{\left (\pi -1\right ) x} = \frac {3 x y^{\pi }}{1-\pi }
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.276 |
|
|
\[
{}2 y^{\prime }+y \cot \left (x \right ) = \frac {8 \cos \left (x \right )^{3}}{y}
\] |
[_Bernoulli] |
✓ |
36.732 |
|
|
\[
{}\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right ) = y^{\sqrt {3}} \sec \left (x \right )
\] |
[_separable] |
✓ |
4.823 |
|
|
\[
{}y^{\prime }+\frac {2 x y}{x^{2}+1} = x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
1.888 |
|
|
\[
{}y^{\prime }+y \cot \left (x \right ) = y^{3} \sin \left (x \right )^{3}
\] |
[_Bernoulli] |
✓ |
3.849 |
|
|
\[
{}y^{\prime } = \left (-y+9 x \right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
2.201 |
|
|
\[
{}y^{\prime } = \left (4 x +y+2\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
6.814 |
|
|
\[
{}y^{\prime } = \sin \left (3 x -3 y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
19.786 |
|
|
\[
{}y^{\prime } = \frac {y \left (\ln \left (x y\right )-1\right )}{x}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.658 |
|
|
\[
{}y^{\prime } = 2 x \left (x +y\right )^{2}-1
\] |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
1.808 |
|
|
\[
{}y^{\prime } = \frac {x +2 y-1}{2 x -y+3}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.822 |
|
|
\[
{}y^{\prime }+p \left (x \right ) y+q \left (x \right ) y^{2} = r \left (x \right )
\] |
[_Riccati] |
✗ |
2.407 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x}-y^{2} = -\frac {2}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.873 |
|
|
\[
{}y^{\prime }+\frac {7 y}{x}-3 y^{2} = \frac {3}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.377 |
|
|
\[
{}\frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right ) = q \left (x \right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.439 |
|
|
\[
{}\frac {y^{\prime }}{y}-\frac {2 \ln \left (y\right )}{x} = \frac {1-2 \ln \left (x \right )}{x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.009 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime }+\frac {\tan \left (y\right )}{2 \sqrt {x +1}} = \frac {1}{2 \sqrt {x +1}}
\] |
[_separable] |
✓ |
30.760 |
|
|
\[
{}y \,{\mathrm e}^{x y}+\left (2 y-x \,{\mathrm e}^{x y}\right ) y^{\prime } = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
1.340 |
|
|
\[
{}\cos \left (x y\right )-x y \sin \left (x y\right )-x^{2} \sin \left (x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
0.315 |
|
|
\[
{}y+3 x^{2}+x y^{\prime } = 0
\] |
[_linear] |
✓ |
0.185 |
|
|
\[
{}2 x \,{\mathrm e}^{y}+\left (3 y^{2}+x^{2} {\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
0.255 |
|
|
\[
{}2 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
0.176 |
|
|
\[
{}y^{2}-2 x +2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
0.316 |
|
|
\[
{}4 \,{\mathrm e}^{2 x}+2 x y-y^{2}+\left (x -y\right )^{2} y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
0.586 |
|
|
\[
{}\frac {1}{x}-\frac {y}{y^{2}+x^{2}}+\frac {x y^{\prime }}{y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _Riccati] |
✓ |
0.347 |
|
|
\[
{}y \cos \left (x y\right )-\sin \left (x \right )+x \cos \left (x y\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.257 |
|
|
\[
{}2 y^{2} {\mathrm e}^{2 x}+3 x^{2}+2 y \,{\mathrm e}^{2 x} y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
0.357 |
|
|
\[
{}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.266 |
|
|
\[
{}\sin \left (y\right )+y \cos \left (x \right )+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
0.256 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.852 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+10 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.880 |
|
|
\[
{}y^{\prime \prime }-36 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.232 |
|
|
\[
{}y^{\prime \prime }+4 y^{\prime } = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.478 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|