|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } = \left (y-1\right ) \left (x +1\right )
\] |
[_separable] |
✓ |
1.570 |
|
|
\[
{}y^{\prime } = {\mathrm e}^{x -y}
\] |
[_separable] |
✓ |
2.428 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{\sqrt {x}}
\] |
[_separable] |
✓ |
12.209 |
|
|
\[
{}y^{\prime } = \frac {\sqrt {y}}{x}
\] |
[_separable] |
✓ |
3.366 |
|
|
\[
{}z^{\prime } = 10^{x +z}
\] |
[_separable] |
✓ |
2.927 |
|
|
\[
{}x^{\prime }+t = 1
\] |
[_quadrature] |
✓ |
0.458 |
|
|
\[
{}y^{\prime } = \cos \left (x -y\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.374 |
|
|
\[
{}y^{\prime }-y = 2 x -3
\] |
[[_linear, ‘class A‘]] |
✓ |
1.316 |
|
|
\[
{}\left (x +2 y\right ) y^{\prime } = 1
\] |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.502 |
|
|
\[
{}y^{\prime }+y = 2 x +1
\] |
[[_linear, ‘class A‘]] |
✓ |
1.263 |
|
|
\[
{}y^{\prime } = \cos \left (x -y-1\right )
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.822 |
|
|
\[
{}y^{\prime }+\sin \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.996 |
|
|
\[
{}y^{\prime } = 2 \sqrt {2 x +y+1}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.094 |
|
|
\[
{}y^{\prime } = \left (x +y+1\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
4.098 |
|
|
\[
{}y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.658 |
|
|
\[
{}\left (1+y^{2}\right ) \left ({\mathrm e}^{2 x}-{\mathrm e}^{y} y^{\prime }\right )-\left (y+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.358 |
|
|
\[
{}x -y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.392 |
|
|
\[
{}y-2 x y+x^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
1.924 |
|
|
\[
{}2 x y^{\prime } = y \left (2 x^{2}-y^{2}\right )
\] |
[_rational, _Bernoulli] |
✓ |
1.560 |
|
|
\[
{}y^{2}+x^{2} y^{\prime } = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
72.921 |
|
|
\[
{}\left (x^{2}+y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.997 |
|
|
\[
{}-y+x y^{\prime } = x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.925 |
|
|
\[
{}x y^{\prime } = y-x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.777 |
|
|
\[
{}-y+x y^{\prime } = \left (x +y\right ) \ln \left (\frac {x +y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.741 |
|
|
\[
{}x y^{\prime } = y \cos \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.415 |
|
|
\[
{}y+\sqrt {x y}-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.131 |
|
|
\[
{}x y^{\prime }-\sqrt {x^{2}-y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
98.532 |
|
|
\[
{}x +y-\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
38.328 |
|
|
\[
{}x^{2}+2 x y-y^{2}+\left (y^{2}+2 x y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
110.095 |
|
|
\[
{}-y+x y^{\prime } = y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.138 |
|
|
\[
{}y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.300 |
|
|
\[
{}y^{2}+x y+x^{2} = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.522 |
|
|
\[
{}\frac {1}{x^{2}-x y+y^{2}} = \frac {y^{\prime }}{2 y^{2}-x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.227 |
|
|
\[
{}y^{\prime } = \frac {2 x y}{3 x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
35.079 |
|
|
\[
{}y^{\prime } = \frac {x}{y}+\frac {y}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.967 |
|
|
\[
{}x y^{\prime } = y+\sqrt {y^{2}-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.525 |
|
|
\[
{}y+\left (2 \sqrt {x y}-x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
43.104 |
|
|
\[
{}x y^{\prime } = y \ln \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.411 |
|
|
\[
{}y^{\prime } \left (y^{\prime }+y\right ) = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
0.531 |
|
|
\[
{}\left (x y^{\prime }+y\right )^{2} = y^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
66.839 |
|
|
\[
{}x^{2} {y^{\prime }}^{2}-3 x y y^{\prime }+2 y^{2} = 0
\] |
[_separable] |
✓ |
0.972 |
|
|
\[
{}-y+x y^{\prime } = \sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.358 |
|
|
\[
{}y {y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
1.721 |
|
|
\[
{}y^{\prime }+\frac {x +2 y}{x} = 0
\] |
[_linear] |
✓ |
2.682 |
|
|
\[
{}y^{\prime } = \frac {y}{x +y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.200 |
|
|
\[
{}x y^{\prime } = x +\frac {y}{2}
\] |
[_linear] |
✓ |
4.207 |
|
|
\[
{}y^{\prime } = \frac {x +y-2}{y-x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.370 |
|
|
\[
{}2 x -4 y+6+\left (x +y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.820 |
|
|
\[
{}y^{\prime } = \frac {2 y-x +5}{2 x -y-4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.653 |
|
|
\[
{}y^{\prime } = -\frac {4 x +3 y+15}{2 x +y+7}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.838 |
|
|
\[
{}y^{\prime } = \frac {x +3 y-5}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.813 |
|
|
\[
{}y^{\prime } = \frac {2 \left (y+2\right )^{2}}{\left (x +y+1\right )^{2}}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
1.898 |
|
|
\[
{}2 x +y+1-\left (4 x +2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.950 |
|
|
\[
{}x -y-1+\left (y-x +2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.910 |
|
|
\[
{}\left (x +4 y\right ) y^{\prime } = 2 x +3 y-5
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.799 |
|
|
\[
{}y+2 = \left (2 x +y-4\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.150 |
|
|
\[
{}\left (y^{\prime }+1\right ) \ln \left (\frac {x +y}{x +3}\right ) = \frac {x +y}{x +3}
\] |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
7.585 |
|
|
\[
{}y^{\prime } = \frac {x -2 y+5}{y-2 x -4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.579 |
|
|
\[
{}y^{\prime } = \frac {3 x -y+1}{2 x +y+4}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.480 |
|
|
\[
{}2 x y^{\prime }+\left (x^{2} y^{4}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.529 |
|
|
\[
{}2 x y^{\prime } \left (x -y^{2}\right )+y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.618 |
|
|
\[
{}x^{3} \left (y^{\prime }-x \right ) = y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
0.396 |
|
|
\[
{}2 x^{2} y^{\prime } = y^{3}+x y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
0.621 |
|
|
\[
{}y+x \left (2 x y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.612 |
|
|
\[
{}2 y^{\prime }+x = 4 \sqrt {y}
\] |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
0.995 |
|
|
\[
{}y^{\prime } = y^{2}-\frac {2}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
0.565 |
|
|
\[
{}2 x y^{\prime }+y = y^{2} \sqrt {x -y^{2} x^{2}}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
5.743 |
|
|
\[
{}\frac {2 x y y^{\prime }}{3} = \sqrt {x^{6}-y^{4}}+y^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
4.505 |
|
|
\[
{}2 y+\left (x^{2} y+1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.576 |
|
|
\[
{}y \left (1+x y\right )+\left (1-x y\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.609 |
|
|
\[
{}y \left (1+y^{2} x^{2}\right )+\left (y^{2} x^{2}-1\right ) x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
0.673 |
|
|
\[
{}\left (x^{2}-y^{4}\right ) y^{\prime }-x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.314 |
|
|
\[
{}y \left (1+\sqrt {x^{2} y^{4}-1}\right )+2 x y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.815 |
|
|
\[
{}x \left (2-9 x y^{2}\right )+y \left (4 y^{2}-6 x^{3}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
2.128 |
|
|
\[
{}\frac {y}{x}+\left (y^{3}+\ln \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
1.544 |
|
|
\[
{}2 x +3+\left (2 y-2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.155 |
|
|
\[
{}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.980 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.142 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}} = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.309 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.521 |
|
|
\[
{}y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+\cos \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.382 |
|
|
\[
{}y^{\prime \prime }+\frac {y^{\prime }}{x}+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.829 |
|
|
\[
{}x^{2} \left (-x^{2}+1\right ) y^{\prime \prime }+2 x \left (-x^{2}+1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.044 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
2.010 |
|
|
\[
{}y^{\prime \prime \prime }-2 x y^{\prime \prime }+4 x^{2} y^{\prime }+8 x^{3} y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
0.048 |
|
|
\[
{}y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y \,{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.532 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x y^{\prime }+4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.758 |
|
|
\[
{}x^{4} y^{\prime \prime \prime \prime }-x^{2} y^{\prime \prime }+y = 0
\] |
[[_high_order, _with_linear_symmetries]] |
✓ |
0.332 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.433 |
|
|
\[
{}y^{\prime \prime }+x y^{\prime }+y = 2 x \,{\mathrm e}^{x}-1
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.345 |
|
|
\[
{}x y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.485 |
|
|
\[
{}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2}+2 x
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.432 |
|
|
\[
{}x^{3} y^{\prime \prime }+x y^{\prime }-y = \cos \left (\frac {1}{x}\right )
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.426 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (x +2\right ) y^{\prime }-y = x +\frac {1}{x}
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.853 |
|
|
\[
{}2 x y^{\prime \prime }+\left (-2+x \right ) y^{\prime }-y = x^{2}-1
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.396 |
|
|
\[
{}x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y = x +\frac {1}{x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
1.991 |
|
|
\[
{}x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y = x \left (1-\ln \left (x \right )\right )^{2}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.045 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+x y = \sec \left (x \right )
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.419 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\frac {y}{4} = -\frac {x^{2}}{2}+\frac {1}{2}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.743 |
|
|
\[
{}\left (\cos \left (x \right )+\sin \left (x \right )\right ) y^{\prime \prime }-2 \cos \left (x \right ) y^{\prime }+\left (\cos \left (x \right )-\sin \left (x \right )\right ) y = \left (\cos \left (x \right )+\sin \left (x \right )\right )^{2} {\mathrm e}^{2 x}
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
268.212 |
|