|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime } = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.589 |
|
|
\[
{}x y^{\prime } = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.461 |
|
|
\[
{}x y^{\prime } = y-\cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
2.289 |
|
|
\[
{}x y^{\prime }+y+2 x \sec \left (x y\right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
5.870 |
|
|
\[
{}x y^{\prime }-y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.534 |
|
|
\[
{}x y^{\prime } = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.168 |
|
|
\[
{}x y^{\prime } = \sin \left (x -y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
3.622 |
|
|
\[
{}x y^{\prime } = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.195 |
|
|
\[
{}x y^{\prime }+\tan \left (y\right ) = 0
\] |
[_separable] |
✓ |
1.895 |
|
|
\[
{}x y^{\prime }+x +\tan \left (x +y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
2.655 |
|
|
\[
{}x y^{\prime } = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
3.422 |
|
|
\[
{}x y^{\prime } = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
2.352 |
|
|
\[
{}x y^{\prime } = y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.470 |
|
|
\[
{}x y^{\prime } = x +y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
9.487 |
|
|
\[
{}x y^{\prime } = y \ln \left (y\right )
\] |
[_separable] |
✓ |
1.608 |
|
|
\[
{}x y^{\prime } = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
4.112 |
|
|
\[
{}x y^{\prime }+\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
2.333 |
|
|
\[
{}x y^{\prime } = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
6.394 |
|
|
\[
{}x y^{\prime }+n y = f \left (x \right ) g \left (x^{n} y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
2.887 |
|
|
\[
{}x y^{\prime } = y f \left (x^{m} y^{n}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
1.345 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (3 x +4\right )+y
\] |
[_linear] |
✓ |
1.015 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
1.325 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = {\mathrm e}^{x} \left (x +1\right )^{n +1}+n y
\] |
[_linear] |
✓ |
1.427 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
3.038 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.691 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.888 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {y+1}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
3.724 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x
\] |
[_quadrature] |
✓ |
0.265 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_linear] |
✓ |
0.855 |
|
|
\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
[_linear] |
✓ |
0.780 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
[_linear] |
✓ |
1.193 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
1.310 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
1.391 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
1.264 |
|
|
\[
{}\left (-x +a \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
2.182 |
|
|
\[
{}2 x y^{\prime } = 2 x^{3}-y
\] |
[_linear] |
✓ |
6.972 |
|
|
\[
{}2 x y^{\prime }+1 = 4 i x y+y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.023 |
|
|
\[
{}2 x y^{\prime } = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
3.043 |
|
|
\[
{}2 x y^{\prime }+y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
4.007 |
|
|
\[
{}2 x y^{\prime } = \left (1+x -6 y^{2}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
1.258 |
|
|
\[
{}2 x y^{\prime }+4 y+a +\sqrt {a^{2}-4 b -4 c y} = 0
\] |
[_separable] |
✓ |
3.985 |
|
|
\[
{}\left (-2 x +1\right ) y^{\prime } = 16+32 x -6 y
\] |
[_linear] |
✓ |
1.607 |
|
|
\[
{}\left (2 x +1\right ) y^{\prime } = 4 \,{\mathrm e}^{-y}-2
\] |
[_separable] |
✓ |
1.610 |
|
|
\[
{}2 \left (1-x \right ) y^{\prime } = 4 x \sqrt {1-x}+y
\] |
[_linear] |
✓ |
1.552 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
2.272 |
|
|
\[
{}3 x y^{\prime } = 3 x^{{2}/{3}}+\left (1-3 y\right ) y
\] |
[_rational, _Riccati] |
✓ |
1.616 |
|
|
\[
{}3 x y^{\prime } = \left (2+x y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.628 |
|
|
\[
{}3 x y^{\prime } = \left (1+3 x y^{3} \ln \left (x \right )\right ) y
\] |
[_Bernoulli] |
✓ |
3.121 |
|
|
\[
{}x^{2} y^{\prime } = -y+a
\] |
[_separable] |
✓ |
0.933 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y
\] |
[_linear] |
✓ |
0.773 |
|
|
\[
{}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y
\] |
[_linear] |
✓ |
0.788 |
|
|
\[
{}x^{2} y^{\prime }+\left (-2 x +1\right ) y = x^{2}
\] |
[_linear] |
✓ |
1.461 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y
\] |
[_linear] |
✓ |
1.100 |
|
|
\[
{}x^{2} y^{\prime } = \left (b x +a \right ) y
\] |
[_separable] |
✓ |
1.089 |
|
|
\[
{}x^{2} y^{\prime }+x \left (x +2\right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2
\] |
[_linear] |
✓ |
1.536 |
|
|
\[
{}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right )
\] |
[_linear] |
✓ |
1.687 |
|
|
\[
{}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
1.762 |
|
|
\[
{}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
2.289 |
|
|
\[
{}x^{2} y^{\prime } = a +b y^{2}
\] |
[_separable] |
✓ |
1.837 |
|
|
\[
{}x^{2} y^{\prime } = \left (x +a y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
14.161 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
21.999 |
|
|
\[
{}x^{2} y^{\prime }+a \,x^{2}+b x y+c y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
72.817 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.103 |
|
|
\[
{}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
1.666 |
|
|
\[
{}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.692 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
1.842 |
|
|
\[
{}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2}
\] |
[_rational, _Riccati] |
✓ |
2.254 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
2.314 |
|
|
\[
{}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2}
\] |
[_rational, _Riccati] |
✓ |
4.639 |
|
|
\[
{}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
1.705 |
|
|
\[
{}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right )
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.826 |
|
|
\[
{}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3}
\] |
[_rational, _Abel] |
✗ |
0.900 |
|
|
\[
{}x^{2} y^{\prime }+y^{2} a +b \,x^{2} y^{3} = 0
\] |
[_rational, _Abel] |
✗ |
0.968 |
|
|
\[
{}x^{2} y^{\prime } = \left (a x +b y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
2.572 |
|
|
\[
{}x^{2} y^{\prime }+x y+\sqrt {y} = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
4.867 |
|
|
\[
{}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
7.043 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-x^{2}+y
\] |
[_linear] |
✓ |
1.290 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+1 = x y
\] |
[_linear] |
✓ |
1.105 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 5-x y
\] |
[_linear] |
✓ |
2.358 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0
\] |
[_linear] |
✓ |
1.036 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
1.872 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0
\] |
[_linear] |
✓ |
1.046 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0
\] |
[_separable] |
✓ |
1.255 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.152 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0
\] |
[_linear] |
✓ |
1.149 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (x^{2}+1\right )-x y
\] |
[_linear] |
✓ |
3.253 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right )
\] |
[_linear] |
✓ |
3.199 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
1.324 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right )
\] |
[_linear] |
✓ |
1.078 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y
\] |
[_linear] |
✓ |
1.637 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y
\] |
[_linear] |
✓ |
2.405 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y
\] |
[_linear] |
✓ |
1.544 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y
\] |
[_linear] |
✓ |
1.030 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y
\] |
[_separable] |
✓ |
1.255 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
1.813 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2}
\] |
[_separable] |
✓ |
1.746 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
1.682 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right )
\] |
[_rational, _Riccati] |
✗ |
6.544 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0
\] |
[_separable] |
✓ |
2.392 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right )
\] |
[_separable] |
✓ |
2.177 |
|