|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\frac {2 y^{{3}/{2}}+1}{\sqrt {x}}+\left (3 \sqrt {x}\, \sqrt {y}-1\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
9.736 |
|
|
\[
{}2 x y-3+\left (x^{2}+4 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.665 |
|
|
\[
{}3 y^{2} x^{2}-y^{3}+2 x +\left (2 x^{3} y-3 x y^{2}+1\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
7.228 |
|
|
\[
{}2 y \sin \left (x \right ) \cos \left (x \right )+y^{2} \sin \left (x \right )+\left (\sin \left (x \right )^{2}-2 y \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
46.792 |
|
|
\[
{}y \,{\mathrm e}^{x}+2 \,{\mathrm e}^{x}+y^{2}+\left ({\mathrm e}^{x}+2 x y\right ) y^{\prime } = 0
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.596 |
|
|
\[
{}\frac {3-y}{x^{2}}+\frac {\left (y^{2}-2 x \right ) y^{\prime }}{x y^{2}} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.513 |
|
|
\[
{}\frac {1+8 x y^{{2}/{3}}}{x^{{2}/{3}} y^{{1}/{3}}}+\frac {\left (2 x^{{4}/{3}} y^{{2}/{3}}-x^{{1}/{3}}\right ) y^{\prime }}{y^{{4}/{3}}} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
3.853 |
|
|
\[
{}4 x +3 y^{2}+2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.750 |
|
|
\[
{}y^{2}+2 x y-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.021 |
|
|
\[
{}y+x \left (x^{2}+y^{2}\right )^{2}+\left (y \left (x^{2}+y^{2}\right )^{2}-x \right ) y^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
2.186 |
|
|
\[
{}4 x y+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.721 |
|
|
\[
{}x y+2 x +y+2+\left (x^{2}+2 x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.998 |
|
|
\[
{}2 r \left (s^{2}+1\right )+\left (r^{4}+1\right ) s^{\prime } = 0
\] |
[_separable] |
✓ |
2.776 |
|
|
\[
{}\csc \left (y\right )+\sec \left (x \right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.029 |
|
|
\[
{}\tan \left (\theta \right )+2 r \theta ^{\prime } = 0
\] |
[_separable] |
✓ |
3.076 |
|
|
\[
{}\left ({\mathrm e}^{v}+1\right ) \cos \left (u \right )+{\mathrm e}^{v} \left (1+\sin \left (u \right )\right ) v^{\prime } = 0
\] |
[_separable] |
✓ |
2.688 |
|
|
\[
{}\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.069 |
|
|
\[
{}x +y-x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.592 |
|
|
\[
{}2 x y+3 y^{2}-\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
118.247 |
|
|
\[
{}v^{3}+\left (u^{3}-u v^{2}\right ) v^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
35.987 |
|
|
\[
{}x \tan \left (\frac {y}{x}\right )+y-x y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.869 |
|
|
\[
{}\left (2 s^{2}+2 s t +t^{2}\right ) s^{\prime }+s^{2}+2 s t -t^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
5.008 |
|
|
\[
{}x^{3}+y^{2} \sqrt {x^{2}+y^{2}}-x y \sqrt {x^{2}+y^{2}}\, y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.658 |
|
|
\[
{}\sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
15.913 |
|
|
\[
{}y+2+y \left (x +4\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.889 |
|
|
\[
{}8 \cos \left (y\right )^{2}+\csc \left (x \right )^{2} y^{\prime } = 0
\] |
[_separable] |
✓ |
2.975 |
|
|
\[
{}\left (3 x +8\right ) \left (y^{2}+4\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
3.602 |
|
|
\[
{}x^{2}+3 y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.215 |
|
|
\[
{}2 x -5 y+\left (4 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.524 |
|
|
\[
{}3 x^{2}+9 x y+5 y^{2}-\left (6 x^{2}+4 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
73.135 |
|
|
\[
{}x +2 y+\left (2 x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.528 |
|
|
\[
{}3 x -y-\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.781 |
|
|
\[
{}x^{2}+2 y^{2}+\left (4 x y-y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
107.096 |
|
|
\[
{}2 x^{2}+2 x y+y^{2}+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
75.517 |
|
|
\[
{}y^{\prime }+\frac {3 y}{x} = 6 x^{2}
\] |
[_linear] |
✓ |
1.635 |
|
|
\[
{}x^{4} y^{\prime }+2 x^{3} y = 1
\] |
[_linear] |
✓ |
1.530 |
|
|
\[
{}y^{\prime }+3 y = 3 x^{2} {\mathrm e}^{-3 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.889 |
|
|
\[
{}y^{\prime }+4 x y = 8 x
\] |
[_separable] |
✓ |
1.519 |
|
|
\[
{}x^{\prime }+\frac {x}{t^{2}} = \frac {1}{t^{2}}
\] |
[_separable] |
✓ |
1.535 |
|
|
\[
{}\left (u^{2}+1\right ) v^{\prime }+4 v u = 3 u
\] |
[_separable] |
✓ |
1.904 |
|
|
\[
{}x y^{\prime }+\frac {\left (2 x +1\right ) y}{x +1} = -1+x
\] |
[_linear] |
✓ |
1.555 |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime }+3 \left (x +1\right ) y = -1+x
\] |
[_linear] |
✓ |
1.652 |
|
|
\[
{}x y^{\prime }+x y+y-1 = 0
\] |
[_linear] |
✓ |
1.259 |
|
|
\[
{}y+\left (x y^{2}+x -y\right ) y^{\prime } = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.294 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )
\] |
[_linear] |
✓ |
1.833 |
|
|
\[
{}\cos \left (t \right ) r^{\prime }+r \sin \left (t \right )-\cos \left (t \right )^{4} = 0
\] |
[_linear] |
✓ |
3.352 |
|
|
\[
{}\cos \left (x \right )^{2}-y \cos \left (x \right )-\left (\sin \left (x \right )+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
3.227 |
|
|
\[
{}y \sin \left (2 x \right )-\cos \left (x \right )+\left (1+\sin \left (x \right )^{2}\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
4.539 |
|
|
\[
{}y^{\prime }-\frac {y}{x} = -\frac {y^{2}}{x}
\] |
[_separable] |
✓ |
2.566 |
|
|
\[
{}x y^{\prime }+y = -2 x^{6} y^{4}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.004 |
|
|
\[
{}y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x = 0
\] |
[_separable] |
✓ |
3.271 |
|
|
\[
{}x^{\prime }+\frac {\left (t +1\right ) x}{2 t} = \frac {t +1}{t x}
\] |
[_separable] |
✓ |
2.428 |
|
|
\[
{}x y^{\prime }-2 y = 2 x^{4}
\] |
[_linear] |
✓ |
2.020 |
|
|
\[
{}y^{\prime }+3 x^{2} y = x^{2}
\] |
[_separable] |
✓ |
1.361 |
|
|
\[
{}{\mathrm e}^{x} \left (y-3 \left ({\mathrm e}^{x}+1\right )^{2}\right )+\left ({\mathrm e}^{x}+1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
2.021 |
|
|
\[
{}2 x \left (y+1\right )-\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.980 |
|
|
\[
{}r^{\prime }+r \tan \left (t \right ) = \cos \left (t \right )^{2}
\] |
[_linear] |
✓ |
2.227 |
|
|
\[
{}x^{\prime }-x = \sin \left (2 t \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
1.895 |
|
|
\[
{}y^{\prime }+\frac {y}{2 x} = \frac {x}{y^{3}}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.730 |
|
|
\[
{}x y^{\prime }+y = \left (x y\right )^{{3}/{2}}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
17.087 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 0 & 1\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.788 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
1.229 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.911 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x <2 \\ 4 & 2\le x \end {array}\right .
\] |
[_linear] |
✓ |
0.739 |
|
|
\[
{}a y^{\prime }+b y = k \,{\mathrm e}^{-\lambda x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.233 |
|
|
\[
{}y^{\prime }+y = 2 \sin \left (x \right )+5 \sin \left (2 x \right )
\] |
[[_linear, ‘class A‘]] |
✓ |
2.310 |
|
|
\[
{}\cos \left (y\right ) y^{\prime }+\frac {\sin \left (y\right )}{x} = 1
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.837 |
|
|
\[
{}\left (y+1\right ) y^{\prime }+x \left (y^{2}+2 y\right ) = x
\] |
[_separable] |
✓ |
1.877 |
|
|
\[
{}y^{\prime } = \left (1-x \right ) y^{2}+\left (2 x -1\right ) y-x
\] |
[_Riccati] |
✓ |
2.563 |
|
|
\[
{}y^{\prime } = -y^{2}+x y+1
\] |
[_Riccati] |
✓ |
1.347 |
|
|
\[
{}y^{\prime } = -8 x y^{2}+4 x \left (4 x +1\right ) y-8 x^{3}-4 x^{2}+1
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.684 |
|
|
\[
{}6 x^{2} y-\left (x^{3}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.712 |
|
|
\[
{}\left (3 y^{2} x^{2}-x \right ) y^{\prime }+2 x y^{3}-y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.217 |
|
|
\[
{}y-1+x \left (x +1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.741 |
|
|
\[
{}x^{2}-2 y+x y^{\prime } = 0
\] |
[_linear] |
✓ |
1.258 |
|
|
\[
{}3 x -5 y+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
10.650 |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}+\left ({\mathrm e}^{2 x} y-2 y\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.260 |
|
|
\[
{}8 x^{3} y-12 x^{3}+\left (x^{4}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
1.918 |
|
|
\[
{}2 x^{2}+x y+y^{2}+2 x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
4.889 |
|
|
\[
{}y^{\prime } = \frac {4 x^{3} y^{2}-3 x^{2} y}{x^{3}-2 x^{4} y}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.204 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+x y = {\mathrm e}^{-x}
\] |
[_linear] |
✓ |
2.123 |
|
|
\[
{}y^{\prime } = \frac {2 x -7 y}{3 y-8 x}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.796 |
|
|
\[
{}x^{2} y^{\prime }+x y = x y^{3}
\] |
[_separable] |
✓ |
5.668 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime }+6 x^{2} y = 6 x^{2}
\] |
[_separable] |
✓ |
1.919 |
|
|
\[
{}y^{\prime } = \frac {2 x^{2}+y^{2}}{2 x y-x^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.181 |
|
|
\[
{}x^{2}+y^{2}-2 x y y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
8.273 |
|
|
\[
{}2 y^{2}+8+\left (-x^{2}+1\right ) y y^{\prime } = 0
\] |
[_separable] |
✓ |
3.576 |
|
|
\[
{}{\mathrm e}^{2 x} y^{2}-2 x +{\mathrm e}^{2 x} y y^{\prime } = 0
\] |
[_exact, _Bernoulli] |
✓ |
3.750 |
|
|
\[
{}3 x^{2}+2 x y^{2}+\left (2 x^{2} y+6 y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
38.005 |
|
|
\[
{}4 x y y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
4.737 |
|
|
\[
{}y^{\prime } = \frac {2 x +7 y}{2 x -2 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.854 |
|
|
\[
{}y^{\prime } = \frac {x y}{x^{2}+1}
\] |
[_separable] |
✓ |
2.369 |
|
|
\[
{}y^{\prime }+y = \left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right .
\] |
[[_linear, ‘class A‘]] |
✓ |
0.811 |
|
|
\[
{}\left (x +2\right ) y^{\prime }+y = \left \{\begin {array}{cc} 2 x & 0\le x \le 2 \\ 4 & 2<x \end {array}\right .
\] |
[_linear] |
✓ |
0.783 |
|
|
\[
{}x^{2} y^{\prime }+x y = \frac {y^{3}}{x}
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
144.209 |
|
|
\[
{}5 x y+4 y^{2}+1+\left (2 x y+x^{2}\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.703 |
|
|
\[
{}2 x +\tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
2.561 |
|
|
\[
{}\left (x +1\right ) y^{2}+y+\left (2 x y+1\right ) y^{\prime } = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.444 |
|
|
\[
{}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0
\] |
[_rational] |
✓ |
2.394 |
|
|
\[
{}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.453 |
|