|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } x = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.188 |
|
|
\[
{}y^{\prime } x = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.570 |
|
|
\[
{}y^{\prime } x = y-\cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.515 |
|
|
\[
{}y^{\prime } x +y+2 x \sec \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
6.040 |
|
|
\[
{}y^{\prime } x -y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.937 |
|
|
\[
{}y^{\prime } x = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.629 |
|
|
\[
{}y^{\prime } x = \sin \left (x -y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.777 |
|
|
\[
{}y^{\prime } x = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.845 |
|
|
\[
{}y^{\prime } x +\tan \left (y\right ) = 0
\] |
[_separable] |
✓ |
2.204 |
|
|
\[
{}y^{\prime } x +x +\tan \left (x +y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.671 |
|
|
\[
{}y^{\prime } x = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.950 |
|
|
\[
{}y^{\prime } x = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.401 |
|
|
\[
{}y^{\prime } x = y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
10.687 |
|
|
\[
{}y^{\prime } x = x +y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.831 |
|
|
\[
{}y^{\prime } x = y \ln \left (y\right )
\] |
[_separable] |
✓ |
1.820 |
|
|
\[
{}y^{\prime } x = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.379 |
|
|
\[
{}y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.423 |
|
|
\[
{}y^{\prime } x = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
7.002 |
|
|
\[
{}y^{\prime } x +n y = f \left (x \right ) g \left (x^{n} y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.843 |
|
|
\[
{}y^{\prime } x = y f \left (x^{m} y^{n}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.330 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (4+3 x \right )+y
\] |
[_linear] |
✓ |
1.274 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
1.565 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = {\mathrm e}^{x} \left (x +1\right )^{n +1}+n y
\] |
[_linear] |
✓ |
1.404 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
2.826 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.887 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
2.087 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.838 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x
\] |
[_quadrature] |
✓ |
0.273 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_linear] |
✓ |
0.843 |
|
|
\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
[_linear] |
✓ |
0.773 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
[_linear] |
✓ |
1.172 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
1.307 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
1.363 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
1.260 |
|
|
\[
{}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.172 |
|
|
\[
{}2 y^{\prime } x = 2 x^{3}-y
\] |
[_linear] |
✓ |
7.497 |
|
|
\[
{}2 y^{\prime } x +1 = 4 i x y+y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.017 |
|
|
\[
{}2 y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.471 |
|
|
\[
{}2 y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
4.389 |
|
|
\[
{}2 y^{\prime } x = \left (1+x -6 y^{2}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.417 |
|
|
\[
{}2 y^{\prime } x +4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
[_separable] |
✓ |
4.020 |
|
|
\[
{}\left (1-2 x \right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
1.950 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
[_separable] |
✓ |
2.256 |
|
|
\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
[_linear] |
✓ |
1.665 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.425 |
|
|
\[
{}3 y^{\prime } x = 3 x^{{2}/{3}}+\left (1-3 y\right ) y
\] |
[_rational, _Riccati] |
✓ |
1.691 |
|
|
\[
{}3 y^{\prime } x = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.852 |
|
|
\[
{}3 y^{\prime } x = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
3.151 |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_separable] |
✓ |
0.918 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y
\] |
[_linear] |
✓ |
0.768 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y
\] |
[_linear] |
✓ |
0.759 |
|
|
\[
{}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2}
\] |
[_linear] |
✓ |
1.695 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
1.102 |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
1.068 |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
[_linear] |
✓ |
1.659 |
|
|
\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
[_linear] |
✓ |
1.821 |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
2.195 |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.528 |
|
|
\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
2.540 |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
14.733 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
21.276 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
109.039 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.057 |
|
|
\[
{}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.959 |
|
|
\[
{}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.688 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.842 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.279 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.261 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.640 |
|
|
\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.881 |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.039 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3}
\] |
[_rational, _Abel] |
✗ |
0.934 |
|
|
\[
{}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
1.005 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.581 |
|
|
\[
{}x^{2} y^{\prime }+x y+\sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
5.015 |
|
|
\[
{}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
8.515 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
[_linear] |
✓ |
1.460 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = x y
\] |
[_linear] |
✓ |
1.279 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
[_linear] |
✓ |
2.680 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0
\] |
[_linear] |
✓ |
1.030 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
1.812 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
1.039 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0
\] |
[_separable] |
✓ |
1.576 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.305 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.334 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
[_linear] |
✓ |
3.555 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
[_linear] |
✓ |
3.470 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.740 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
[_linear] |
✓ |
1.266 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
[_linear] |
✓ |
1.864 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y
\] |
[_linear] |
✓ |
2.582 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y
\] |
[_linear] |
✓ |
1.708 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y
\] |
[_linear] |
✓ |
1.033 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
1.287 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
2.138 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
2.075 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.798 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right )
\] |
[_rational, _Riccati] |
✗ |
7.686 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
2.658 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
2.156 |
|