|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 y = \left (x^{2} y^{4}+x \right ) y^{\prime }
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.178 |
|
|
\[
{}1+x y \left (x y^{2}+1\right ) y^{\prime } = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
10.843 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x y = x \left (-x^{2}+1\right ) \sqrt {y}
\] |
[_rational, _Bernoulli] |
✗ |
15.823 |
|
|
\[
{}\left (1-x \right ) y^{\prime }-y-1 = 0
\] |
[_separable] |
✓ |
1.527 |
|
|
\[
{}y^{2}+\left (x y+x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
5.973 |
|
|
\[
{}2 x +y-\left (x -2 y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.671 |
|
|
\[
{}x \ln \left (x \right ) y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
1.136 |
|
|
\[
{}x -2 y+1+\left (y-2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.796 |
|
|
\[
{}2 x y-2 x y^{3}+x^{3}+\left (x^{2}+y^{2}-3 x^{2} y^{2}\right ) y^{\prime } = 0
\] |
[_exact, _rational] |
✓ |
1.665 |
|
|
\[
{}2 \,{\mathrm e}^{x}-t^{2}+t \,{\mathrm e}^{x} x^{\prime } = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.312 |
|
|
\[
{}2 y+6 = x y y^{\prime }
\] |
[_separable] |
✓ |
1.843 |
|
|
\[
{}x -3 y = \left (3 y-x +2\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.336 |
|
|
\[
{}y \sin \left (x \right )-2 \cos \left (y\right )+\tan \left (x \right )-\left (\cos \left (x \right )-2 x \sin \left (y\right )+\sin \left (y\right )\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
42.111 |
|
|
\[
{}x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
8.874 |
|
|
\[
{}y-x y^{\prime } = 2 y^{2}+2 y^{\prime }
\] |
[_separable] |
✓ |
1.740 |
|
|
\[
{}\tan \left (y\right ) = \left (3 x +4\right ) y^{\prime }
\] |
[_separable] |
✓ |
2.451 |
|
|
\[
{}y^{\prime }+y \ln \left (y\right ) \tan \left (x \right ) = 2 y
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.325 |
|
|
\[
{}2 x y+y^{4}+\left (x y^{3}-2 x^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.408 |
|
|
\[
{}y+\left (-2 y+3 x \right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
13.201 |
|
|
\[
{}r^{\prime } = r \cot \left (\theta \right )
\] |
[_separable] |
✓ |
1.378 |
|
|
\[
{}\left (3 x +4 y\right ) y^{\prime }+2 x +y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.543 |
|
|
\[
{}2 x^{3}-y^{3}-3 x +3 x y^{2} y^{\prime } = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.747 |
|
|
\[
{}x y^{\prime }-y-\sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.569 |
|
|
\[
{}y^{\prime } = \cos \left (y\right ) \cos \left (x \right )^{2}
\] |
[_separable] |
✓ |
2.067 |
|
|
\[
{}x +y+\left (2 x +3 y-1\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.807 |
|
|
\[
{}1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
4.184 |
|
|
\[
{}y^{\prime }+x +y \cot \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.188 |
|
|
\[
{}-6+3 x = x y y^{\prime }
\] |
[_separable] |
✓ |
1.248 |
|
|
\[
{}x -2 x y+{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
1.657 |
|
|
\[
{}2 x y^{\prime }-y+\frac {x^{2}}{y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.589 |
|
|
\[
{}x y^{\prime }+y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
3.919 |
|
|
\[
{}y \sqrt {y^{2}+x^{2}}+x y = x^{2} y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.022 |
|
|
\[
{}3 \,{\mathrm e}^{x} \tan \left (y\right ) = \left (1-{\mathrm e}^{x}\right ) \sec \left (y\right )^{2} y^{\prime }
\] |
[_separable] |
✓ |
2.984 |
|
|
\[
{}\sec \left (y\right )^{2} y^{\prime } = \tan \left (y\right )+2 x \,{\mathrm e}^{x}
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.470 |
|
|
\[
{}2 x \tan \left (y\right )+3 y^{2}+x^{2}+\left (x^{2} \sec \left (y\right )^{2}+6 x y-y^{2}\right ) y^{\prime } = 0
\] |
[_exact] |
✓ |
50.432 |
|
|
\[
{}y \cos \left (\frac {x}{y}\right )-\left (y+x \cos \left (\frac {x}{y}\right )\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.816 |
|
|
\[
{}y \left (3 x^{2}+y\right )-x \left (x^{2}-y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.896 |
|
|
\[
{}x +\left (2 x +3 y+2\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
2.233 |
|
|
\[
{}x y^{\prime }-5 y-x \sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.632 |
|
|
\[
{}x \sqrt {1-y}-\sqrt {-x^{2}+1}\, y^{\prime } = 0
\] |
[_separable] |
✓ |
2.618 |
|
|
\[
{}x y-y^{2}-x^{2} y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
2.773 |
|
|
\[
{}x \,{\mathrm e}^{-y^{2}}+y y^{\prime } = 0
\] |
[_separable] |
✓ |
1.837 |
|
|
\[
{}\frac {2 y^{3}-2 y^{3} x^{2}-x +x y^{2} \ln \left (y\right )}{x y^{2}}+\frac {\left (2 y^{3} \ln \left (x \right )-y^{3} x^{2}+2 x +x y^{2}\right ) y^{\prime }}{y^{3}} = 0
\] |
[_exact] |
✓ |
4.841 |
|
|
\[
{}x y^{\prime }-2 y-2 x^{4} y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.511 |
|
|
\[
{}\left (-2 x^{2}-3 x y\right ) y^{\prime }+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.050 |
|
|
\[
{}x y^{\prime } = x^{4}+4 y
\] |
[_linear] |
✓ |
1.277 |
|
|
\[
{}y+x y^{\prime } = x^{3} y^{6}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
8.022 |
|
|
\[
{}x^{\prime } = x+x^{2} {\mathrm e}^{\theta }
\] |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
1.608 |
|
|
\[
{}y^{2}+x^{2} = 2 x y y^{\prime }
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
9.232 |
|
|
\[
{}3 x y+\left (3 x^{2}+y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
37.858 |
|
|
\[
{}y^{\prime }+2 y = 3 \,{\mathrm e}^{2 x}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.346 |
|
|
\[
{}4 x y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0
\] |
[_separable] |
✓ |
2.291 |
|
|
\[
{}x -2 y+3 = \left (x -2 y+1\right ) y^{\prime }
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.666 |
|
|
\[
{}y^{2}+\left (x^{3}-2 x y\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.324 |
|
|
\[
{}2 x y-2 y+1+x \left (x -1\right ) y^{\prime } = 0
\] |
[_linear] |
✓ |
1.465 |
|
|
\[
{}y^{3}+2 x^{2} y+\left (-3 x^{3}-2 x y^{2}\right ) y^{\prime } = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
348.429 |
|
|
\[
{}2 \left (x^{2}+1\right ) y^{\prime } = \left (2 y^{2}-1\right ) x y
\] |
[_separable] |
✓ |
13.618 |
|
|
\[
{}y^{\prime }-y = 0
\] |
[_quadrature] |
✓ |
0.963 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.317 |
|
|
\[
{}y^{\prime \prime }+7 y^{\prime }+12 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.895 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.898 |
|
|
\[
{}y^{\prime \prime }-7 y^{\prime }+6 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.928 |
|
|
\[
{}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.942 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.136 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.148 |
|
|
\[
{}y^{\prime \prime }-3 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.250 |
|
|
\[
{}2 y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
1.245 |
|
|
\[
{}2 y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }+12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.076 |
|
|
\[
{}y^{\prime \prime \prime \prime }-6 y^{\prime \prime }+8 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime }+6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }-17 y^{\prime }+60 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime }-9 y^{\prime \prime }+23 y^{\prime }-15 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.077 |
|
|
\[
{}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-7 y^{\prime \prime }-y^{\prime }+6 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}2 y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-20 y^{\prime \prime }+27 y^{\prime }+18 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}12 y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.087 |
|
|
\[
{}y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime } = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.072 |
|
|
\[
{}4 y^{\prime \prime \prime }+2 y^{\prime \prime }-4 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime }-5 y^{\prime \prime }-2 y^{\prime }+24 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-7 y^{\prime \prime }-8 y^{\prime }+12 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+15 y^{\prime \prime }+4 y^{\prime }-12 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.088 |
|
|
\[
{}y^{\left (5\right )}+y^{\prime \prime \prime \prime }-13 y^{\prime \prime \prime }-13 y^{\prime \prime }+36 y^{\prime }+36 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }-15 y^{\prime \prime \prime }-19 y^{\prime \prime }+30 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.086 |
|
|
\[
{}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.084 |
|
|
\[
{}y^{\left (5\right )}+3 y^{\prime \prime \prime }+2 y^{\prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.091 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.965 |
|
|
\[
{}y^{\prime \prime } = 0
\] |
[[_2nd_order, _quadrature]] |
✓ |
1.426 |
|
|
\[
{}2 y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-3 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.080 |
|
|
\[
{}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}y^{\prime \prime \prime \prime } = 0
\] |
[[_high_order, _quadrature]] |
✓ |
0.042 |
|
|
\[
{}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}4 y^{\prime \prime \prime }-3 y^{\prime }+y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.078 |
|
|
\[
{}4 y^{\left (5\right )}-3 y^{\prime \prime \prime }-y^{\prime \prime } = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.083 |
|
|
\[
{}y^{\prime \prime \prime }-7 y^{\prime \prime }+16 y^{\prime }-12 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}4 y^{\prime \prime \prime }-8 y^{\prime \prime }+5 y^{\prime }-y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.079 |
|
|
\[
{}y^{\prime \prime \prime \prime }-y = 0
\] |
[[_high_order, _missing_x]] |
✓ |
0.082 |
|
|
\[
{}y^{\prime \prime \prime }-8 y = 0
\] |
[[_3rd_order, _missing_x]] |
✓ |
0.085 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+3 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
2.247 |
|