|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
6.582 |
|
|
\[
{}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.871 |
|
|
\[
{}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
12.877 |
|
|
\[
{}y+2+y \left (x +4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.877 |
|
|
\[
{}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
3.009 |
|
|
\[
{}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.300 |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.177 |
|
|
\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.580 |
|
|
\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
101.094 |
|
|
\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.802 |
|
|
\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.042 |
|
|
\[
{}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
134.829 |
|
|
\[
{}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.127 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
[_linear] |
✓ |
1.655 |
|
|
\[
{}x^{4} y^{\prime }+2 x^{3} y = 1
\] |
[_linear] |
✓ |
1.502 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.671 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.431 |
|
|
\[
{}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}}
\] |
[_separable] |
✓ |
1.443 |
|
|
\[
{}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u
\] |
[_separable] |
✓ |
1.595 |
|
|
\[
{}y^{\prime } x +\frac {\left (2 x +1\right ) y}{x +1} = x -1
\] |
[_linear] |
✓ |
1.378 |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y = x -1
\] |
[_linear] |
✓ |
1.584 |
|
|
\[
{}y^{\prime } x +x y+y-1 = 0
\] |
[_linear] |
✓ |
1.153 |
|
|
\[
{}y+\left (x y^{2}+x -y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.205 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.724 |
|
|
\[
{}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0
\] |
[_linear] |
✓ |
3.059 |
|
|
\[
{}\cos \left (x \right )^{2}-y \cos \left (x \right )-\left (1+\sin \left (x \right )\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
2.901 |
|
|
\[
{}y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
4.173 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x}
\] |
[_separable] |
✓ |
2.357 |
|
|
\[
{}y^{\prime } x +y = -2 x^{6} y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.426 |
|
|
\[
{}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0
\] |
[_separable] |
✓ |
2.664 |
|
|
\[
{}x^{\prime }+\frac {\left (1+t \right ) x}{2 t} = \frac {1+t}{t x}
\] |
[_separable] |
✓ |
2.019 |
|
|
\[
{}y^{\prime } x -2 y = 2 x^{4}
\] |
[_linear] |
✓ |
1.971 |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
1.261 |
|
|
\[
{}{\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.912 |
|
|
\[
{}2 x \left (1+y\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.770 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
2.118 |
|
|
\[
{}x^{\prime }-x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.657 |
|
|
\[
{}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.407 |
|
|
\[
{}y^{\prime } x +y = \left (x y\right )^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
494.115 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.694 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.833 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.654 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\] |
[_linear] |
✓ |
0.664 |
|
|
\[
{}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.103 |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (x \right )+5 \sin \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.112 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x} = 1
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.734 |
|
|
\[
{}\left (1+y\right ) y^{\prime }+x \left (y^{2}+2 y\right ) = x
\] |
[_separable] |
✓ |
1.885 |
|
|
\[
{}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x
\] |
[_Riccati] |
✓ |
2.141 |
|
|
\[
{}y^{\prime } = -y^{2}+x y+1
\] |
[_Riccati] |
✓ |
1.240 |
|
|
\[
{}y^{\prime } = -8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.419 |
|
|
\[
{}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.851 |
|
|
\[
{}\left (3 x^{2} y^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.681 |
|
|
\[
{}y-1+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.587 |
|
|
\[
{}x^{2}-2 y+y^{\prime } x = 0
\] |
[_linear] |
✓ |
1.207 |
|
|
\[
{}3 x -5 y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.392 |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.246 |
|
|
\[
{}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.615 |
|
|
\[
{}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
3.941 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.508 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+x y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.009 |
|
|
\[
{}y^{\prime } = \frac {2 x -7 y}{3 y-8 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.447 |
|
|
\[
{}x^{2} y^{\prime }+x y = x y^{3}
\] |
[_separable] |
✓ |
4.372 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2}
\] |
[_separable] |
✓ |
1.641 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
15.227 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
10.018 |
|
|
\[
{}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.163 |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}-2 x +{\mathrm e}^{2 x} y y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
3.163 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
19.559 |
|
|
\[
{}4 x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
4.250 |
|
|
\[
{}y^{\prime } = \frac {2 x +7 y}{2 x -2 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.069 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+1}
\] |
[_separable] |
✓ |
2.421 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.653 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\] |
[_linear] |
✓ |
0.664 |
|
|
\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
160.372 |
|
|
\[
{}5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.456 |
|
|
\[
{}2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.100 |
|
|
\[
{}y^{2} \left (x +1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.248 |
|
|
\[
{}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.254 |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.205 |
|
|
\[
{}8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.868 |
|
|
\[
{}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.276 |
|
|
\[
{}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.839 |
|
|
\[
{}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.444 |
|
|
\[
{}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.957 |
|
|
\[
{}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.048 |
|
|
\[
{}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
11.635 |
|
|
\[
{}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.211 |
|
|
\[
{}4 x +3 y+1+\left (x +y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.277 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.598 |
|
|
\[
{}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x}
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
280.479 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.598 |
|
|
\[
{}y^{\prime \prime }-4 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.082 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.484 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.083 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.504 |
|
|
\[
{}y^{\prime \prime }-5 y^{\prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.072 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 y^{\prime } x -8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.124 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.303 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }-3 \left (x +1\right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.315 |
|