|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}3 y^{\prime } = x +\sqrt {x^{2}-3 y}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
56.401 |
|
|
\[
{}y^{\prime } x = \sqrt {a^{2}-x^{2}}
\] |
[_quadrature] |
✓ |
1.211 |
|
|
\[
{}y^{\prime } x +x +y = 0
\] |
[_linear] |
✓ |
8.443 |
|
|
\[
{}y^{\prime } x +x^{2}-y = 0
\] |
[_linear] |
✓ |
11.283 |
|
|
\[
{}y^{\prime } x = x^{3}-y
\] |
[_linear] |
✓ |
4.145 |
|
|
\[
{}y^{\prime } x = 1+x^{3}+y
\] |
[_linear] |
✓ |
2.132 |
|
|
\[
{}y^{\prime } x = x^{m}+y
\] |
[_linear] |
✓ |
11.588 |
|
|
\[
{}y^{\prime } x = x \sin \left (x \right )-y
\] |
[_linear] |
✓ |
2.901 |
|
|
\[
{}y^{\prime } x = x^{2} \sin \left (x \right )+y
\] |
[_linear] |
✓ |
2.998 |
|
|
\[
{}y^{\prime } x = x^{n} \ln \left (x \right )-y
\] |
[_linear] |
✓ |
12.623 |
|
|
\[
{}y^{\prime } x = \sin \left (x \right )-2 y
\] |
[_linear] |
✓ |
2.855 |
|
|
\[
{}y^{\prime } x = a y
\] |
[_separable] |
✓ |
16.548 |
|
|
\[
{}y^{\prime } x = 1+x +a y
\] |
[_linear] |
✓ |
7.419 |
|
|
\[
{}y^{\prime } x = a x +b y
\] |
[_linear] |
✓ |
18.184 |
|
|
\[
{}y^{\prime } x = a \,x^{2}+b y
\] |
[_linear] |
✓ |
13.885 |
|
|
\[
{}y^{\prime } x = a +b \,x^{n}+c y
\] |
[_linear] |
✓ |
5.133 |
|
|
\[
{}y^{\prime } x +2+\left (3-x \right ) y = 0
\] |
[_linear] |
✓ |
2.394 |
|
|
\[
{}y^{\prime } x +x +\left (a x +2\right ) y = 0
\] |
[_linear] |
✓ |
10.868 |
|
|
\[
{}y^{\prime } x +\left (b x +a \right ) y = 0
\] |
[_separable] |
✓ |
5.897 |
|
|
\[
{}y^{\prime } x = x^{3}+\left (-2 x^{2}+1\right ) y
\] |
[_linear] |
✓ |
11.534 |
|
|
\[
{}y^{\prime } x = a x -\left (-b \,x^{2}+1\right ) y
\] |
[_linear] |
✓ |
3.119 |
|
|
\[
{}y^{\prime } x +x +\left (-a \,x^{2}+2\right ) y = 0
\] |
[_linear] |
✓ |
2.802 |
|
|
\[
{}y^{\prime } x +x^{2}+y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
1.020 |
|
|
\[
{}y^{\prime } x = x^{2}+y \left (1+y\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
15.005 |
|
|
\[
{}y^{\prime } x -y+y^{2} = x^{{2}/{3}}
\] |
[_rational, _Riccati] |
✓ |
11.288 |
|
|
\[
{}y^{\prime } x = a +b y^{2}
\] |
[_separable] |
✓ |
19.751 |
|
|
\[
{}y^{\prime } x = a \,x^{2}+y+b y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
7.594 |
|
|
\[
{}y^{\prime } x = a \,x^{2 n}+\left (n +b y\right ) y
\] |
[_rational, _Riccati] |
✓ |
13.755 |
|
|
\[
{}y^{\prime } x = a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
7.437 |
|
|
\[
{}y^{\prime } x = k +a \,x^{n}+b y+c y^{2}
\] |
[_rational, _Riccati] |
✓ |
16.677 |
|
|
\[
{}y^{\prime } x +a +x y^{2} = 0
\] |
[_rational, [_Riccati, _special]] |
✓ |
3.224 |
|
|
\[
{}y^{\prime } x +\left (1-y x \right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
3.577 |
|
|
\[
{}y^{\prime } x = \left (1-y x \right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
17.543 |
|
|
\[
{}y^{\prime } x = \left (y x +1\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
18.118 |
|
|
\[
{}y^{\prime } x = a \,x^{3} \left (1-y x \right ) y
\] |
[_Bernoulli] |
✓ |
4.011 |
|
|
\[
{}y^{\prime } x = x^{3}+\left (2 x^{2}+1\right ) y+x y^{2}
\] |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
14.478 |
|
|
\[
{}y^{\prime } x = y \left (2 y x +1\right )
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
5.725 |
|
|
\[
{}y^{\prime } x +b x +\left (2+a x y\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
11.899 |
|
|
\[
{}y^{\prime } x +\operatorname {a0} +\operatorname {a1} x +\left (\operatorname {a2} +\operatorname {a3} x y\right ) y = 0
\] |
[_rational, _Riccati] |
✓ |
11.724 |
|
|
\[
{}y^{\prime } x +a \,x^{2} y^{2}+2 y = b
\] |
[_rational, _Riccati] |
✓ |
13.852 |
|
|
\[
{}y^{\prime } x +x^{m}+\frac {\left (n -m \right ) y}{2}+x^{n} y^{2} = 0
\] |
[_rational, _Riccati] |
✓ |
7.260 |
|
|
\[
{}y^{\prime } x +\left (a +b \,x^{n} y\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
17.970 |
|
|
\[
{}y^{\prime } x = a \,x^{m}-b y-c \,x^{n} y^{2}
\] |
[_rational, _Riccati] |
✓ |
20.937 |
|
|
\[
{}y^{\prime } x = 2 x -y+a \,x^{n} \left (x -y\right )^{2}
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
10.115 |
|
|
\[
{}y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y = 0
\] |
[_Bernoulli] |
✓ |
21.169 |
|
|
\[
{}y^{\prime } x = y+\left (x^{2}-y^{2}\right ) f \left (x \right )
\] |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
15.862 |
|
|
\[
{}y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
35.010 |
|
|
\[
{}y^{\prime } x +y \left (1-x y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
25.945 |
|
|
\[
{}y^{\prime } x +y = a \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
14.572 |
|
|
\[
{}y^{\prime } x = a y+b \left (x^{2}+1\right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
22.339 |
|
|
\[
{}y^{\prime } x +2 y = a \,x^{2 k} y^{k}
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
44.626 |
|
|
\[
{}y^{\prime } x = 4 y-4 \sqrt {y}
\] |
[_separable] |
✓ |
40.062 |
|
|
\[
{}y^{\prime } x +2 y = \sqrt {1+y^{2}}
\] |
[_separable] |
✓ |
32.279 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}+y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
57.112 |
|
|
\[
{}y^{\prime } x = y+\sqrt {x^{2}-y^{2}}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
186.401 |
|
|
\[
{}y^{\prime } x = y+x \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.334 |
|
|
\[
{}y^{\prime } x = y-x \left (x -y\right ) \sqrt {x^{2}+y^{2}}
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.933 |
|
|
\[
{}y^{\prime } x = y+a \sqrt {y^{2}+b^{2} x^{2}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
83.473 |
|
|
\[
{}y^{\prime } x +\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right ) = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
13.674 |
|
|
\[
{}y^{\prime } x +x -y+x \cos \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
18.938 |
|
|
\[
{}y^{\prime } x = y-x \cos \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
30.942 |
|
|
\[
{}y^{\prime } x = \left (-2 x^{2}+1\right ) \cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
7.982 |
|
|
\[
{}y^{\prime } x = y-\cot \left (y\right )^{2}
\] |
[_separable] |
✓ |
16.060 |
|
|
\[
{}y^{\prime } x +y+2 x \sec \left (y x \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
40.779 |
|
|
\[
{}y^{\prime } x -y+x \sec \left (\frac {y}{x}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
69.468 |
|
|
\[
{}y^{\prime } x = y+x \sec \left (\frac {y}{x}\right )^{2}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
75.328 |
|
|
\[
{}y^{\prime } x = \sin \left (x -y\right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
14.290 |
|
|
\[
{}y^{\prime } x = y+x \sin \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
22.454 |
|
|
\[
{}y^{\prime } x +\tan \left (y\right ) = 0
\] |
[_separable] |
✓ |
14.355 |
|
|
\[
{}y^{\prime } x +x +\tan \left (x +y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
20.954 |
|
|
\[
{}y^{\prime } x = y-x \tan \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
24.107 |
|
|
\[
{}y^{\prime } x = \left (1+y^{2}\right ) \left (x^{2}+\arctan \left (y\right )\right )
\] |
[‘y=_G(x,y’)‘] |
✓ |
13.167 |
|
|
\[
{}y^{\prime } x = y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
82.944 |
|
|
\[
{}y^{\prime } x = x +y+x \,{\mathrm e}^{\frac {y}{x}}
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
86.986 |
|
|
\[
{}y^{\prime } x = y \ln \left (y\right )
\] |
[_separable] |
✓ |
9.492 |
|
|
\[
{}y^{\prime } x = \left (1+\ln \left (x \right )-\ln \left (y\right )\right ) y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
41.155 |
|
|
\[
{}y^{\prime } x +\left (1-\ln \left (x \right )-\ln \left (y\right )\right ) y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
23.062 |
|
|
\[
{}y^{\prime } x = y-2 x \tanh \left (\frac {y}{x}\right )
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
64.237 |
|
|
\[
{}y^{\prime } x +n y = f \left (x \right ) g \left (x^{n} y\right )
\] |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
1.277 |
|
|
\[
{}y^{\prime } x = y f \left (x^{m} y^{n}\right )
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
16.603 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = x^{3} \left (4+3 x \right )+y
\] |
[_linear] |
✓ |
2.145 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (x +1\right )^{4}+2 y
\] |
[_linear] |
✓ |
11.148 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = {\mathrm e}^{x} \left (x +1\right )^{n +1}+n y
\] |
[_linear] |
✓ |
3.645 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = a y+b x y^{2}
\] |
[_rational, _Bernoulli] |
✓ |
19.182 |
|
|
\[
{}\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3} = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
22.773 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = \left (1-x y^{3}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
14.295 |
|
|
\[
{}\left (x +1\right ) y^{\prime } = 1+y+\left (x +1\right ) \sqrt {1+y}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
25.486 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x
\] |
[_quadrature] |
✓ |
0.868 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +y
\] |
[_linear] |
✓ |
11.665 |
|
|
\[
{}\left (x +a \right ) y^{\prime }+b \,x^{2}+y = 0
\] |
[_linear] |
✓ |
2.947 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = 2 \left (x +a \right )^{5}+3 y
\] |
[_linear] |
✓ |
4.721 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b +c y
\] |
[_separable] |
✓ |
14.730 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = b x +c y
\] |
[_linear] |
✓ |
14.357 |
|
|
\[
{}\left (x +a \right ) y^{\prime } = y \left (1-a y\right )
\] |
[_separable] |
✓ |
14.562 |
|
|
\[
{}\left (a -x \right ) y^{\prime } = y+\left (c x +b \right ) y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
17.161 |
|
|
\[
{}2 y^{\prime } x = 2 x^{3}-y
\] |
[_linear] |
✓ |
55.142 |
|
|
\[
{}2 y^{\prime } x +1 = 4 i x y+y^{2}
\] |
[_rational, _Riccati] |
✓ |
10.407 |
|
|
\[
{}2 y^{\prime } x = y \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
16.017 |
|
|
\[
{}2 y^{\prime } x +y \left (1+y^{2}\right ) = 0
\] |
[_separable] |
✓ |
18.355 |
|
|
\[
{}2 y^{\prime } x = \left (1+x -6 y^{2}\right ) y
\] |
[_rational, _Bernoulli] |
✓ |
3.271 |
|