|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime }-\sqrt {\frac {1+y^{3}}{x^{3}+1}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.768 |
|
|
\[
{}y^{\prime }-\frac {\sqrt {{| y \left (-1+y\right ) \left (-1+a y\right )|}}}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}} = 0
\] |
[_separable] |
✓ |
44.011 |
|
|
\[
{}y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}} = 0
\] |
[_separable] |
✓ |
3.295 |
|
|
\[
{}y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
20.970 |
|
|
\[
{}y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
13.220 |
|
|
\[
{}y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
7.742 |
|
|
\[
{}y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
6.811 |
|
|
\[
{}y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right ) = 0
\] |
[_separable] |
✓ |
1.926 |
|
|
\[
{}y^{\prime }-\left (\frac {a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{a_{3} y^{3}+a_{2} y^{2}+a_{1} y+a_{0}}\right )^{{2}/{3}} = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
3.204 |
|
|
\[
{}y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.059 |
|
|
\[
{}y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x} = 0
\] |
[_separable] |
✓ |
1.367 |
|
|
\[
{}y^{\prime }-a \cos \left (y\right )+b = 0
\] |
[_quadrature] |
✓ |
0.569 |
|
|
\[
{}y^{\prime }-\cos \left (b x +a y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
54.520 |
|
|
\[
{}y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.042 |
|
|
\[
{}y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.602 |
|
|
\[
{}y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1 = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.204 |
|
|
\[
{}y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1 = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.487 |
|
|
\[
{}y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.731 |
|
|
\[
{}y^{\prime }-\tan \left (y x \right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
0.628 |
|
|
\[
{}y^{\prime }-f \left (a x +b y\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
1.080 |
|
|
\[
{}y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.824 |
|
|
\[
{}y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )} = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
1.613 |
|
|
\[
{}y^{\prime }-\frac {y a f \left (x^{c} y\right )+c \,x^{a} y^{b}}{x b f \left (x^{c} y\right )-x^{a} y^{b}} = 0
\] |
[NONE] |
✗ |
3.526 |
|
|
\[
{}2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x} = 0
\] |
[_Riccati] |
✗ |
13.050 |
|
|
\[
{}y^{\prime } x -\sqrt {a^{2}-x^{2}} = 0
\] |
[_quadrature] |
✓ |
0.493 |
|
|
\[
{}y^{\prime } x +y-x \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.116 |
|
|
\[
{}y^{\prime } x -y-\frac {x}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
1.068 |
|
|
\[
{}y^{\prime } x -y-x^{2} \sin \left (x \right ) = 0
\] |
[_linear] |
✓ |
1.139 |
|
|
\[
{}y^{\prime } x -y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )} = 0
\] |
[_linear] |
✓ |
2.824 |
|
|
\[
{}y^{\prime } x +a y+b \,x^{n} = 0
\] |
[_linear] |
✓ |
1.165 |
|
|
\[
{}y^{\prime } x +y^{2}+x^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.070 |
|
|
\[
{}y^{\prime } x -y^{2}+1 = 0
\] |
[_separable] |
✓ |
1.323 |
|
|
\[
{}y^{\prime } x +a y^{2}-y+b \,x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.193 |
|
|
\[
{}y^{\prime } x +a y^{2}-b y+c \,x^{2 b} = 0
\] |
[_rational, _Riccati] |
✓ |
1.967 |
|
|
\[
{}y^{\prime } x +a y^{2}-b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
1.972 |
|
|
\[
{}y^{\prime } x +x y^{2}+a = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
1.052 |
|
|
\[
{}y^{\prime } x +x y^{2}-y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.743 |
|
|
\[
{}y^{\prime } x +x y^{2}-y-a \,x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.198 |
|
|
\[
{}y^{\prime } x +x y^{2}-\left (2 x^{2}+1\right ) y-x^{3} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
2.866 |
|
|
\[
{}y^{\prime } x +a x y^{2}+2 y+b x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.370 |
|
|
\[
{}y^{\prime } x +a x y^{2}+b y+c x +d = 0
\] |
[_rational, _Riccati] |
✓ |
4.214 |
|
|
\[
{}y^{\prime } x +x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b} = 0
\] |
[_rational, _Riccati] |
✓ |
2.403 |
|
|
\[
{}y^{\prime } x +a \,x^{\alpha } y^{2}+b y-c \,x^{\beta } = 0
\] |
[_rational, _Riccati] |
✓ |
2.958 |
|
|
\[
{}y^{\prime } x -y^{2} \ln \left (x \right )+y = 0
\] |
[_Bernoulli] |
✓ |
2.159 |
|
|
\[
{}y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right ) = 0
\] |
[_Bernoulli] |
✓ |
2.176 |
|
|
\[
{}y^{\prime } x +f \left (x \right ) \left (y^{2}-x^{2}\right ) = 0
\] |
[_Riccati] |
✗ |
1.416 |
|
|
\[
{}y^{\prime } x +y^{3}+3 x y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.518 |
|
|
\[
{}y^{\prime } x -\sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.894 |
|
|
\[
{}y^{\prime } x +a \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
11.290 |
|
|
\[
{}y^{\prime } x -x \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.295 |
|
|
\[
{}y^{\prime } x -x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.973 |
|
|
\[
{}y^{\prime } x -x \,{\mathrm e}^{\frac {y}{x}}-y-x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.323 |
|
|
\[
{}y^{\prime } x -y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.501 |
|
|
\[
{}y^{\prime } x -y \left (\ln \left (y x \right )-1\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.645 |
|
|
\[
{}y^{\prime } x -y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
1.475 |
|
|
\[
{}y^{\prime } x -\sin \left (x -y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
2.504 |
|
|
\[
{}y^{\prime } x +\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.593 |
|
|
\[
{}y^{\prime } x -x \sin \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.076 |
|
|
\[
{}y^{\prime } x +x \cos \left (\frac {y}{x}\right )-y+x = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
2.892 |
|
|
\[
{}y^{\prime } x +x \tan \left (\frac {y}{x}\right )-y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.316 |
|
|
\[
{}y^{\prime } x -y f \left (y x \right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
0.881 |
|
|
\[
{}y^{\prime } x -y f \left (x^{a} y^{b}\right ) = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.304 |
|
|
\[
{}y^{\prime } x +a y-f \left (x \right ) g \left (x^{a} y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.289 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+\left (-x +y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.331 |
|
|
\[
{}2 y^{\prime } x -y-2 x^{3} = 0
\] |
[_linear] |
✓ |
1.835 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2 = 0
\] |
[_separable] |
✓ |
1.466 |
|
|
\[
{}3 y^{\prime } x -3 x \ln \left (x \right ) y^{4}-y = 0
\] |
[_Bernoulli] |
✓ |
3.149 |
|
|
\[
{}x^{2} y^{\prime }+y-x = 0
\] |
[_linear] |
✓ |
0.970 |
|
|
\[
{}x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_linear] |
✓ |
1.382 |
|
|
\[
{}x^{2} y^{\prime }-\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
1.264 |
|
|
\[
{}x^{2} y^{\prime }+y^{2}+y x +x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.678 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-y x = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
1.810 |
|
|
\[
{}x^{2} y^{\prime }-y^{2}-y x -x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.971 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right ) = 0
\] |
[_rational, _Riccati] |
✓ |
2.205 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2 = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.569 |
|
|
\[
{}x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.561 |
|
|
\[
{}x^{2} \left (y^{\prime }-y^{2}\right )-y a \,x^{2}+a x +2 = 0
\] |
[_rational, _Riccati] |
✓ |
1.710 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )-b = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.423 |
|
|
\[
{}x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c = 0
\] |
[_rational, _Riccati] |
✓ |
2.331 |
|
|
\[
{}x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.529 |
|
|
\[
{}x^{2} y^{\prime }+x y^{3}+a y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.524 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2} y^{3}+b y^{2} = 0
\] |
[_rational, _Abel] |
✗ |
0.572 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x -1 = 0
\] |
[_linear] |
✓ |
1.029 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right ) = 0
\] |
[_linear] |
✓ |
3.335 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2} = 0
\] |
[_linear] |
✓ |
1.096 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right ) = 0
\] |
[_rational, _Abel] |
✗ |
0.804 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2} = 0
\] |
[‘y=_G(x,y’)‘] |
✗ |
4.758 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-y x +a = 0
\] |
[_linear] |
✓ |
2.063 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right ) = 0
\] |
[_linear] |
✓ |
2.755 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1 = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.558 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-\left (-x +y\right ) y = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.520 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right ) = 0
\] |
[_rational, _Riccati] |
✗ |
4.543 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x = 0
\] |
[_separable] |
✓ |
2.382 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.438 |
|
|
\[
{}\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.573 |
|
|
\[
{}\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2} = 0
\] |
[_linear] |
✓ |
1.408 |
|
|
\[
{}\left (x -a \right ) \left (x -b \right ) y^{\prime }+y^{2}+k \left (y+x -a \right ) \left (y+x -b \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
3.069 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.579 |
|
|
\[
{}2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x = 0
\] |
[_rational, _Riccati] |
✓ |
1.745 |
|
|
\[
{}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
2.297 |
|