|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2}+3 y^{\prime } x = y^{3}+2 y
\] |
[_rational, _Abel] |
✓ |
17.499 |
|
|
\[
{}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5
\] |
[_separable] |
✓ |
4.670 |
|
|
\[
{}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2
\] |
[_separable] |
✓ |
4.936 |
|
|
\[
{}x +y = y^{\prime } x
\] |
[_linear] |
✓ |
1.743 |
|
|
\[
{}\left (x +y\right ) y^{\prime }+x = y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.565 |
|
|
\[
{}y^{\prime } x -y = \sqrt {y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.996 |
|
|
\[
{}y^{\prime } = \frac {2 x -y}{x +4 y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
6.340 |
|
|
\[
{}y^{\prime } x -y = \sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
109.239 |
|
|
\[
{}x +y y^{\prime } = 2 y
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.338 |
|
|
\[
{}y^{\prime } x -y+\sqrt {y^{2}-x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.516 |
|
|
\[
{}x^{2}+y^{2} = x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
6.996 |
|
|
\[
{}\left (y x -x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
10.961 |
|
|
\[
{}y+y^{\prime } x = 2 \sqrt {y x}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.359 |
|
|
\[
{}x +y+\left (x -y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.875 |
|
|
\[
{}y \left (x^{2}-y x +y^{2}\right )+x y^{\prime } \left (x^{2}+y x +y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
127.997 |
|
|
\[
{}y^{\prime } x -y-x \sin \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.175 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\cosh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.554 |
|
|
\[
{}x^{2}+y^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
20.777 |
|
|
\[
{}\left (\frac {x}{y}+\frac {y}{x}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.194 |
|
|
\[
{}x \,{\mathrm e}^{\frac {y}{x}}+y = y^{\prime } x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.532 |
|
|
\[
{}y^{\prime } = \frac {x +y}{x -y}
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.343 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
8.357 |
|
|
\[
{}\left (3 y x -2 x^{2}\right ) y^{\prime } = 2 y^{2}-y x
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
19.069 |
|
|
\[
{}y^{\prime } = \frac {y}{x -k \sqrt {x^{2}+y^{2}}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
88.855 |
|
|
\[
{}y^{2} \left (y y^{\prime }-x \right )+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
83.027 |
|
|
\[
{}y^{\prime } = \frac {y}{x}+\tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
13.847 |
|
|
\[
{}x +y-\left (x -y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.936 |
|
|
\[
{}x +\left (x -2 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
9.557 |
|
|
\[
{}2 x -y+1+\left (x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.460 |
|
|
\[
{}x -y+2+\left (x +y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.988 |
|
|
\[
{}x -y+\left (y-x +1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.435 |
|
|
\[
{}y^{\prime } = \frac {x +y-1}{x -y-1}
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.985 |
|
|
\[
{}x +y+\left (2 x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.382 |
|
|
\[
{}x -y+1+\left (x -y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.227 |
|
|
\[
{}x +2 y+\left (3 x +6 y+3\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.402 |
|
|
\[
{}x +2 y+2 = \left (2 x +y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.053 |
|
|
\[
{}3 x -y+1+\left (x -3 y-5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
16.339 |
|
|
\[
{}6 x -3 y+6+\left (2 x -y+5\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.143 |
|
|
\[
{}2 x +3 y+2+\left (-x +y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
18.351 |
|
|
\[
{}x +y+4 = \left (2 x +2 y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.210 |
|
|
\[
{}2 x +3 y-1+\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.331 |
|
|
\[
{}3 x -y+2+\left (x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
12.078 |
|
|
\[
{}3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
88.625 |
|
|
\[
{}x -2 y+3+\left (1-x +2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.405 |
|
|
\[
{}2 x +y+\left (4 x +2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.248 |
|
|
\[
{}2 x +y+\left (4 x -2 y+1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
37.089 |
|
|
\[
{}x +y+\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
14.442 |
|
|
\[
{}3 x +y+\left (x +3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.122 |
|
|
\[
{}a_{1} x +b_{1} y+c_{1} +\left (b_{1} x +b_{2} y+c_{2} \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
9.315 |
|
|
\[
{}x \left (6 y x +5\right )+\left (2 x^{3}+3 y\right ) y^{\prime } = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.479 |
|
|
\[
{}3 x^{2} y+x y^{2}+{\mathrm e}^{x}+\left (x^{3}+x^{2} y+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
3.778 |
|
|
\[
{}2 y x -\left (x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
19.012 |
|
|
\[
{}y \cos \left (x \right )-2 \sin \left (y\right ) = \left (2 x \cos \left (y\right )-\sin \left (x \right )\right ) y^{\prime }
\] |
[_exact] |
✓ |
31.404 |
|
|
\[
{}\frac {2 y x -1}{y}+\frac {\left (x +3 y\right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
4.645 |
|
|
\[
{}y \,{\mathrm e}^{x}-2 x +{\mathrm e}^{x} y^{\prime } = 0
\] |
[[_linear, ‘class A‘]] |
✓ |
1.600 |
|
|
\[
{}3 y \sin \left (x \right )-\cos \left (y\right )+\left (x \sin \left (y\right )-3 \cos \left (x \right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
124.383 |
|
|
\[
{}x y^{2}+2 y+\left (2 y^{3}-x^{2} y+2 x \right ) y^{\prime } = 0
\] |
[_rational] |
✗ |
1.125 |
|
|
\[
{}\frac {2}{y}-\frac {y}{x^{2}}+\left (\frac {1}{x}-\frac {2 x}{y^{2}}\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
4.130 |
|
|
\[
{}\frac {y x +1}{y}+\frac {\left (2 y-x \right ) y^{\prime }}{y^{2}} = 0
\] |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.454 |
|
|
\[
{}\frac {y \left (2+x^{3} y\right )}{x^{3}} = \frac {\left (1-2 x^{3} y\right ) y^{\prime }}{x^{2}}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
9.177 |
|
|
\[
{}y^{2} \csc \left (x \right )^{2}+6 y x -2 = \left (2 y \cot \left (x \right )-3 x^{2}\right ) y^{\prime }
\] |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
86.097 |
|
|
\[
{}\frac {2 y}{x^{3}}+\frac {2 x}{y^{2}} = \left (\frac {1}{x^{2}}+\frac {2 x^{2}}{y^{3}}\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
10.331 |
|
|
\[
{}\cos \left (y\right )-\left (x \sin \left (y\right )-y^{2}\right ) y^{\prime } = 0
\] |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
16.596 |
|
|
\[
{}2 y \sin \left (y x \right )+\left (2 x \sin \left (y x \right )+y^{3}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
114.174 |
|
|
\[
{}\frac {x \cos \left (\frac {x}{y}\right )}{y}+\sin \left (\frac {x}{y}\right )+\cos \left (x \right )-\frac {x^{2} \cos \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0
\] |
[_exact] |
✓ |
17.924 |
|
|
\[
{}y \,{\mathrm e}^{y x}+2 y x +\left (x \,{\mathrm e}^{y x}+x^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
6.174 |
|
|
\[
{}\frac {x^{2}+3 y^{2}}{x \left (3 x^{2}+4 y^{2}\right )}+\frac {\left (2 x^{2}+y^{2}\right ) y^{\prime }}{y \left (3 x^{2}+4 y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
80.030 |
|
|
\[
{}\frac {x^{2}-y^{2}}{x \left (2 x^{2}+y^{2}\right )}+\frac {\left (x^{2}+2 y^{2}\right ) y^{\prime }}{y \left (2 x^{2}+y^{2}\right )} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
96.158 |
|
|
\[
{}\frac {2 x^{2}}{x^{2}+y^{2}}+\ln \left (x^{2}+y^{2}\right )+\frac {2 x y y^{\prime }}{x^{2}+y^{2}} = 0
\] |
[_exact] |
✓ |
2.684 |
|
|
\[
{}y^{\prime } x +\ln \left (x \right )-y = 0
\] |
[_linear] |
✓ |
3.402 |
|
|
\[
{}y x +\left (y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.681 |
|
|
\[
{}\left (x -2 y x \right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
2.269 |
|
|
\[
{}x^{2} y+y^{2}+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.526 |
|
|
\[
{}x y^{3}-1+x^{2} y^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.416 |
|
|
\[
{}\left (x^{3} y^{3}-1\right ) y^{\prime }+x^{2} y^{4} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.405 |
|
|
\[
{}y \left (y-x^{2}\right )+x^{3} y^{\prime } = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
3.347 |
|
|
\[
{}y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.459 |
|
|
\[
{}\left (x -x \sqrt {x^{2}-y^{2}}\right ) y^{\prime }-y = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.667 |
|
|
\[
{}2 y x +\left (y-x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.033 |
|
|
\[
{}y = x \left (x^{2} y-1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
15.288 |
|
|
\[
{}{\mathrm e}^{x} y^{\prime } = 2 x y^{2}+y \,{\mathrm e}^{x}
\] |
[_Bernoulli] |
✓ |
3.828 |
|
|
\[
{}\left (x^{2}+y^{2}+x \right ) y^{\prime } = y
\] |
[_rational] |
✓ |
1.168 |
|
|
\[
{}\left (2 x +3 x^{2} y\right ) y^{\prime }+y+2 x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.830 |
|
|
\[
{}2 x^{2} y y^{\prime }+x^{4} {\mathrm e}^{x}-2 x y^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
2.466 |
|
|
\[
{}y \left (1-x^{4} y^{2}\right )+y^{\prime } x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
7.547 |
|
|
\[
{}y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.029 |
|
|
\[
{}x^{2} y^{2}-y+\left (2 x^{3} y+x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.113 |
|
|
\[
{}\left (x^{2}+y^{2}-2 y\right ) y^{\prime } = 2 x
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.384 |
|
|
\[
{}y-x^{2} \sqrt {x^{2}-y^{2}}-y^{\prime } x = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.214 |
|
|
\[
{}y \left (x +y^{2}\right )+x \left (x -y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
25.275 |
|
|
\[
{}y^{\prime } x +2 y = x^{2}
\] |
[_linear] |
✓ |
2.395 |
|
|
\[
{}y^{\prime }-y x = {\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right )
\] |
[_linear] |
✓ |
4.280 |
|
|
\[
{}y^{\prime }+2 y x = 2 x \,{\mathrm e}^{-x^{2}}
\] |
[_linear] |
✓ |
2.437 |
|
|
\[
{}y^{\prime } = y+3 x^{2} {\mathrm e}^{x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.643 |
|
|
\[
{}x^{\prime }+x = {\mathrm e}^{-y}
\] |
[[_linear, ‘class A‘]] |
✓ |
0.779 |
|
|
\[
{}y x^{\prime }+\left (1+y \right ) x = {\mathrm e}^{y}
\] |
[_linear] |
✓ |
3.945 |
|
|
\[
{}y+\left (2 x -3 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
16.770 |
|
|
\[
{}y^{\prime } x -2 x^{4}-2 y = 0
\] |
[_linear] |
✓ |
2.463 |
|
|
\[
{}1 = \left ({\mathrm e}^{y}+x \right ) y^{\prime }
\] |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
3.605 |
|
|
\[
{}y^{2} x^{\prime }+\left (y^{2}+2 y \right ) x = 1
\] |
[_linear] |
✓ |
2.161 |
|