|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.632 |
|
|
\[
{}y^{\prime } x = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.537 |
|
|
\[
{}y^{\prime } x = y-\cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
3.145 |
|
|
\[
{}y^{\prime } x +y+2 x \sec \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
8.443 |
|
|
\[
{}y^{\prime } x -y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.283 |
|
|
\[
{}y^{\prime } x = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.363 |
|
|
\[
{}y^{\prime } x = \sin \left (x -y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.425 |
|
|
\[
{}y^{\prime } x = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.901 |
|
|
\[
{}y^{\prime } x +\tan \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.943 |
|
|
\[
{}y^{\prime } x +x +\tan \left (x +y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.401 |
|
|
\[
{}y^{\prime } x = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.481 |
|
|
\[
{}y^{\prime } x = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.489 |
|
|
\[
{}y^{\prime } x = {\mathrm e}^{\frac {y}{x}} x +y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.913 |
|
|
\[
{}y^{\prime } x = x +y+{\mathrm e}^{\frac {y}{x}} x
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
5.793 |
|
|
\[
{}y^{\prime } x = y \ln \left (y\right )
\] |
[_separable] |
✓ |
1.685 |
|
|
\[
{}y^{\prime } x = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.618 |
|
|
\[
{}y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.184 |
|
|
\[
{}y^{\prime } x = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
133.764 |
|
|
\[
{}y^{\prime } x +n y = f \left (x \right ) g \left (x^{n} y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
3.323 |
|
|
\[
{}y^{\prime } x = y f \left (x^{m} y^{n}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.619 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (3 x +4\right )+y
\] |
[_linear] |
✓ |
0.998 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
1.354 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = {\mathrm e}^{x} \left (x +1\right )^{n +1}+n y
\] |
[_linear] |
✓ |
1.842 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
3.670 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
3.240 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
2.009 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.301 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x
\] |
[_quadrature] |
✓ |
0.361 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_linear] |
✓ |
1.123 |
|
|
\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
[_linear] |
✓ |
1.015 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
[_linear] |
✓ |
1.531 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
1.497 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
2.234 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
1.547 |
|
|
\[
{}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.787 |
|
|
\[
{}2 y^{\prime } x = 2 x^{3}-y
\] |
[_linear] |
✓ |
6.986 |
|
|
\[
{}2 y^{\prime } x +1 = 4 i x y+y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.479 |
|
|
\[
{}2 y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.808 |
|
|
\[
{}2 y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
5.408 |
|
|
\[
{}2 y^{\prime } x = \left (1+x -6 y^{2}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.505 |
|
|
\[
{}2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
[_separable] |
✓ |
4.180 |
|
|
\[
{}\left (-2 x +1\right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
1.775 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
[_separable] |
✓ |
2.106 |
|
|
\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
[_linear] |
✓ |
1.722 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.730 |
|
|
\[
{}3 y^{\prime } x = 3 x^{{2}/{3}}+\left (1-3 y\right ) y
\] |
[_rational, _Riccati] |
✓ |
1.954 |
|
|
\[
{}3 y^{\prime } x = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
23.499 |
|
|
\[
{}3 y^{\prime } x = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
3.418 |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_separable] |
✓ |
1.071 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y
\] |
[_linear] |
✓ |
0.964 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y
\] |
[_linear] |
✓ |
0.954 |
|
|
\[
{}x^{2} y^{\prime }+\left (-2 x +1\right ) y = x^{2}
\] |
[_linear] |
✓ |
1.600 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
1.468 |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
1.385 |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
[_linear] |
✓ |
1.797 |
|
|
\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
[_linear] |
✓ |
1.974 |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.646 |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.904 |
|
|
\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
2.928 |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
3.139 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
38.032 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
139.107 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.743 |
|
|
\[
{}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.654 |
|
|
\[
{}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
2.263 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
2.012 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.840 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.262 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2}
\] |
[_rational, _Riccati] |
✓ |
3.449 |
|
|
\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.044 |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.589 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3}
\] |
[_rational, _Abel] |
✗ |
1.212 |
|
|
\[
{}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.529 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.859 |
|
|
\[
{}x^{2} y^{\prime }+x y+\sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
6.669 |
|
|
\[
{}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
8.035 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
[_linear] |
✓ |
1.438 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = x y
\] |
[_linear] |
✓ |
1.261 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
[_linear] |
✓ |
1.327 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0
\] |
[_linear] |
✓ |
1.213 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
2.840 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
1.185 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0
\] |
[_separable] |
✓ |
1.242 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.315 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.298 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
[_linear] |
✓ |
3.838 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
[_linear] |
✓ |
3.709 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.198 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
[_linear] |
✓ |
1.138 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
[_linear] |
✓ |
1.661 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y
\] |
[_linear] |
✓ |
2.527 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y
\] |
[_linear] |
✓ |
1.729 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y
\] |
[_linear] |
✓ |
1.275 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
1.746 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.879 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
1.829 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.780 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right )
\] |
[_rational, _Riccati] |
✗ |
4.256 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
3.335 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
3.136 |
|