|
# |
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] |
✓ |
55.238 |
|
|
\[
{}\left (x +2 y+2 y^{3} x^{2}+x y^{4}\right ) y^{\prime }+\left (1+y^{4}\right ) y = 0
\] |
[_rational] |
✓ |
991.852 |
|
|
\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.474 |
|
|
\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.516 |
|
|
\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.787 |
|
|
\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.411 |
|
|
\[
{}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0
\] |
[_rational] |
✓ |
1.565 |
|
|
\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.243 |
|
|
\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.332 |
|
|
\[
{}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n} = 0
\] |
[_Bernoulli] |
✗ |
4.390 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}}
\] |
[_separable] |
✓ |
1.889 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}-y^{2}} = \sqrt {a^{2}-x^{2}}
\] |
[_separable] |
✓ |
2.177 |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
19.321 |
|
|
\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.654 |
|
|
\[
{}y^{\prime } \sqrt {x y}+x -y = \sqrt {x y}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.448 |
|
|
\[
{}\left (x -2 \sqrt {x y}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
98.035 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.680 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.677 |
|
|
\[
{}\left (x -\sqrt {y^{2}+x^{2}}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.935 |
|
|
\[
{}x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.292 |
|
|
\[
{}x \left (x +\sqrt {y^{2}+x^{2}}\right ) y^{\prime }+y \sqrt {y^{2}+x^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
70.388 |
|
|
\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
22.987 |
|
|
\[
{}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (y^{2}+x^{2}\right )\right ) y^{\prime } = x \left (y^{2}+x^{2}\right )+y \sqrt {1+x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.496 |
|
|
\[
{}y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right ) = 0
\] |
unknown |
✓ |
39.924 |
|
|
\[
{}\left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right ) = 0
\] |
[_exact] |
✓ |
37.059 |
|
|
\[
{}\left (x +\cos \left (x \right ) \sec \left (y\right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right ) = 0
\] |
[NONE] |
✓ |
42.227 |
|
|
\[
{}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.575 |
|
|
\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.023 |
|
|
\[
{}\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
1.450 |
|
|
\[
{}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.351 |
|
|
\[
{}\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right ) = 0
\] |
[_exact] |
✓ |
36.632 |
|
|
\[
{}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0
\] |
[_separable] |
✓ |
6.838 |
|
|
\[
{}{y^{\prime }}^{2} = a \,x^{n}
\] |
[_quadrature] |
✓ |
0.291 |
|
|
\[
{}{y^{\prime }}^{2} = y
\] |
[_quadrature] |
✓ |
0.536 |
|
|
\[
{}{y^{\prime }}^{2} = x -y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.480 |
|
|
\[
{}{y^{\prime }}^{2} = y+x^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.166 |
|
|
\[
{}{y^{\prime }}^{2}+x^{2} = 4 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.563 |
|
|
\[
{}{y^{\prime }}^{2}+3 x^{2} = 8 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.240 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{2}+b y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.344 |
|
|
\[
{}{y^{\prime }}^{2} = 1+y^{2}
\] |
[_quadrature] |
✓ |
0.554 |
|
|
\[
{}{y^{\prime }}^{2} = 1-y^{2}
\] |
[_quadrature] |
✓ |
0.563 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2}-y^{2}
\] |
[_quadrature] |
✓ |
0.661 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{2}
\] |
[_quadrature] |
✓ |
1.214 |
|
|
\[
{}{y^{\prime }}^{2} = a +b y^{2}
\] |
[_quadrature] |
✓ |
1.357 |
|
|
\[
{}{y^{\prime }}^{2} = x^{2} y^{2}
\] |
[_separable] |
✓ |
2.385 |
|
|
\[
{}{y^{\prime }}^{2} = \left (y-1\right ) y^{2}
\] |
[_quadrature] |
✓ |
3.993 |
|
|
\[
{}{y^{\prime }}^{2} = \left (y-a \right ) \left (y-b \right ) \left (y-c \right )
\] |
[_quadrature] |
✓ |
34.592 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} y^{n}
\] |
[_quadrature] |
✓ |
3.780 |
|
|
\[
{}{y^{\prime }}^{2} = a^{2} \left (1-\ln \left (y\right )^{2}\right ) y^{2}
\] |
[_quadrature] |
✓ |
3.257 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.809 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
0.946 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right ) \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.105 |
|
|
\[
{}{y^{\prime }}^{2}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right ) \left (y-c \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
1.838 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-a \right ) \left (y-b \right ) \left (y-c \right )^{2}
\] |
[_separable] |
✓ |
1.643 |
|
|
\[
{}{y^{\prime }}^{2} = f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
10.811 |
|
|
\[
{}{y^{\prime }}^{2}+2 y^{\prime }+x = 0
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }+a \left (x -y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
0.447 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime }-y^{2} = 0
\] |
[_quadrature] |
✓ |
0.440 |
|
|
\[
{}{y^{\prime }}^{2}-5 y^{\prime }+6 = 0
\] |
[_quadrature] |
✓ |
0.842 |
|
|
\[
{}{y^{\prime }}^{2}-7 y^{\prime }+12 = 0
\] |
[_quadrature] |
✓ |
0.842 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b = 0
\] |
[_quadrature] |
✓ |
0.211 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b x = 0
\] |
[_quadrature] |
✓ |
0.222 |
|
|
\[
{}{y^{\prime }}^{2}+a y^{\prime }+b y = 0
\] |
[_quadrature] |
✓ |
0.818 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.347 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.333 |
|
|
\[
{}{y^{\prime }}^{2}-x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.439 |
|
|
\[
{}{y^{\prime }}^{2}+x y^{\prime }+x -y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.490 |
|
|
\[
{}{y^{\prime }}^{2}+\left (1-x \right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.435 |
|
|
\[
{}{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.381 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2-x \right ) y^{\prime }+1-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.472 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.474 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+1 = 0
\] |
[_quadrature] |
✓ |
0.304 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-3 x^{2} = 0
\] |
[_quadrature] |
✓ |
0.490 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.437 |
|
|
\[
{}{y^{\prime }}^{2}+2 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.434 |
|
|
\[
{}{y^{\prime }}^{2}-2 x y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.336 |
|
|
\[
{}{y^{\prime }}^{2}-\left (2 x +1\right ) y^{\prime }-x \left (1-x \right ) = 0
\] |
[_quadrature] |
✓ |
0.226 |
|
|
\[
{}{y^{\prime }}^{2}+2 \left (1-x \right ) y^{\prime }-2 x +2 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.470 |
|
|
\[
{}{y^{\prime }}^{2}+3 x y^{\prime }-y = 0
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
0.455 |
|
|
\[
{}{y^{\prime }}^{2}-4 \left (x +1\right ) y^{\prime }+4 y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.406 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime } = b c \,x^{2}
\] |
[_quadrature] |
✓ |
0.214 |
|
|
\[
{}{y^{\prime }}^{2}-a x y^{\prime }+a y = 0
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.382 |
|
|
\[
{}{y^{\prime }}^{2}+a x y^{\prime }+b \,x^{2}+c y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
3.567 |
|
|
\[
{}{y^{\prime }}^{2}+\left (b x +a \right ) y^{\prime }+c = b y
\] |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
0.579 |
|
|
\[
{}{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y^{\prime } = 0
\] |
[_quadrature] |
✓ |
0.626 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.188 |
|
|
\[
{}{y^{\prime }}^{2}-2 a \,x^{3} y^{\prime }+4 a \,x^{2} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.032 |
|
|
\[
{}{y^{\prime }}^{2}+4 x^{5} y^{\prime }-12 x^{4} y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.372 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } \cosh \left (x \right )+1 = 0
\] |
[_quadrature] |
✓ |
0.376 |
|
|
\[
{}{y^{\prime }}^{2}+y^{\prime } y = \left (x +y\right ) x
\] |
[_quadrature] |
✓ |
1.139 |
|
|
\[
{}{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.365 |
|
|
\[
{}{y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+x y = 0
\] |
[_quadrature] |
✓ |
1.204 |
|
|
\[
{}{y^{\prime }}^{2}-2 y^{\prime } y-2 x = 0
\] |
[_dAlembert] |
✓ |
44.766 |
|
|
\[
{}{y^{\prime }}^{2}+\left (2 y+1\right ) y^{\prime }+y \left (y-1\right ) = 0
\] |
[_quadrature] |
✓ |
0.670 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (x -y\right ) y^{\prime }-4 x y = 0
\] |
[_quadrature] |
✓ |
1.271 |
|
|
\[
{}{y^{\prime }}^{2}-\left (1+4 y\right ) y^{\prime }+\left (1+4 y\right ) y = 0
\] |
[_quadrature] |
✓ |
1.106 |
|
|
\[
{}{y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y = 0
\] |
[_quadrature] |
✓ |
1.369 |
|
|
\[
{}{y^{\prime }}^{2}+\left (a +6 y\right ) y^{\prime }+y \left (3 a +b +9 y\right ) = 0
\] |
[_quadrature] |
✓ |
1.111 |
|
|
\[
{}{y^{\prime }}^{2}+a y y^{\prime }-a x = 0
\] |
[_dAlembert] |
✓ |
1.626 |
|