|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
19.604 |
|
|
\[
{}\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+\left (1+y^{4}\right ) y = 0
\] |
[_rational] |
✓ |
100.476 |
|
|
\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
7.046 |
|
|
\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
15.757 |
|
|
\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.184 |
|
|
\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.289 |
|
|
\[
{}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0
\] |
[_rational] |
✓ |
1.833 |
|
|
\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
4.855 |
|
|
\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.615 |
|
|
\[
{}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n} = 0
\] |
[_Bernoulli] |
✗ |
4.944 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}}
\] |
[_separable] |
✓ |
2.034 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}-y^{2}} = \sqrt {a^{2}-x^{2}}
\] |
[_separable] |
✓ |
2.270 |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
66.038 |
|
|
\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.569 |
|
|
\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
33.194 |
|
|
\[
{}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
24.385 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.950 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.902 |
|
|
\[
{}\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
18.819 |
|
|
\[
{}x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.949 |
|
|
\[
{}x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
193.199 |
|
|
\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
42.096 |
|
|
\[
{}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime } = x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.125 |
|
|
\[
{}y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right ) = 0
\] |
unknown |
✓ |
39.572 |
|
|
\[
{}\left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right ) = 0
\] |
[_exact] |
✓ |
37.986 |
|
|
\[
{}\left (x +\cos \left (x \right ) \sec \left (y\right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right ) = 0
\] |
[NONE] |
✓ |
43.296 |
|
|
\[
{}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.942 |
|
|
\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.309 |
|
|
\[
{}\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
1.727 |
|
|
\[
{}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.707 |
|
|
\[
{}\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right ) = 0
\] |
[_exact] |
✓ |
36.172 |
|
|
\[
{}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0
\] |
[_separable] |
✓ |
8.996 |
|
|
\[
{}{y^{\prime }}^{2} = a \,x^{n}
\] |
[_quadrature] |
✓ |
0.433 |
|
|
\[
{}{y^{\prime }}^{2} = y
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}{y^{\prime }}^{2} = x -y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.705 |
|
|
\[
{}{y^{\prime }}^{2} = x^{2}+y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.507 |
|
|
\[
{}{y^{\prime }}^{2}+x^{2} = 4 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.570 |
|
|
\[
{}{y^{\prime }}^{2}+3 x^{2} = 8 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.592 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{2}+b y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.710 |
|
|
\[
{}{y^{\prime }}^{2} = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.862 |
|
|
\[
{}{y^{\prime }}^{2} = 1-y^{2}
\] |
[_quadrature] |
✓ |
0.685 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2}-y^{2}
\] |
[_quadrature] |
✓ |
0.843 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{2}
\] |
[_quadrature] |
✓ |
0.957 |
|
|
\[
{}{y^{\prime }}^{2} = a +b y^{2}
\] |
[_quadrature] |
✓ |
1.176 |
|
|
\[
{}{y^{\prime }}^{2} = y^{2} x^{2}
\] |
[_separable] |
✓ |
2.446 |
|
|
\[
{}{y^{\prime }}^{2} = \left (y-1\right ) y^{2}
\] |
[_quadrature] |
✓ |
15.083 |
|
|
\[
{}{y^{\prime }}^{2} = \left (y-a \right ) \left (y-b \right ) \left (y-c \right )
\] |
[_quadrature] |
✓ |
70.980 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{n}
\] |
[_quadrature] |
✓ |
0.783 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2}
\] |
[_quadrature] |
✓ |
0.868 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.104 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.092 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.507 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.095 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2}
\] |
[_separable] |
✓ |
1.577 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
12.788 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.187 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.444 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
11.882 |
|
|
\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
0.352 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
0.332 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b = 0
\] |
[_quadrature] |
✓ |
0.190 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b x = 0
\] |
[_quadrature] |
✓ |
0.201 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b y = 0
\] |
[_quadrature] |
✓ |
0.495 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.268 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.414 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.405 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.452 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }+x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.500 |
|
|
\[
{}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.428 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.424 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.479 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.462 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.299 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.406 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.458 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.447 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.405 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right ) = 0
\] |
[_quadrature] |
✓ |
0.210 |
|
|
\[
{}{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.492 |
|
|
\[
{}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.502 |
|
|
\[
{}{y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.442 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime } = b c \,x^{2}
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.477 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.624 |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.664 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.353 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.580 |
|
|
\[
{}{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.179 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.803 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
[_quadrature] |
✓ |
0.388 |
|
|
\[
{}{y^{\prime }}^{2}+y y^{\prime } = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
0.502 |
|
|
\[
{}{y^{\prime }}^{2}-y y^{\prime }+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.914 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
0.518 |
|
|
\[
{}{y^{\prime }}^{2}-2 y y^{\prime }-2 x = 0
\] |
[_dAlembert] |
✓ |
41.984 |
|
|
\[
{}{y^{\prime }}^{2}+\left (2 y+1\right ) y^{\prime }+y \left (y-1\right ) = 0
\] |
[_quadrature] |
✓ |
0.421 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 x y = 0
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+4 y\right ) y^{\prime }+\left (1+4 y\right ) y = 0
\] |
[_quadrature] |
✓ |
1.135 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y = 0
\] |
[_quadrature] |
✓ |
38.253 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0
\] |
[_quadrature] |
✓ |
39.197 |
|
|
\[
{}{y^{\prime }}^{2}+a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
1.809 |
|