|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}y^{\prime } y+f \left (y^{2}+x^{2}\right ) g \left (x \right )+x = 0
\] |
[NONE] |
✗ |
2.920 |
|
|
\[
{}\left (y+1\right ) y^{\prime }-y-x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
5.153 |
|
|
\[
{}\left (y-1+x \right ) y^{\prime }-y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.527 |
|
|
\[
{}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.002 |
|
|
\[
{}\left (y-2 x +1\right ) y^{\prime }+y+x = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.996 |
|
|
\[
{}\left (y-x^{2}\right ) y^{\prime }-x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
0.981 |
|
|
\[
{}\left (y-x^{2}\right ) y^{\prime }+4 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.037 |
|
|
\[
{}\left (y+g \left (x \right )\right ) y^{\prime }-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
7.852 |
|
|
\[
{}2 y^{\prime } y-x y^{2}-x^{3} = 0
\] |
[_rational, _Bernoulli] |
✓ |
1.387 |
|
|
\[
{}\left (2 y+x +1\right ) y^{\prime }-x -2 y+1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.325 |
|
|
\[
{}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.861 |
|
|
\[
{}\left (2 y-x \right ) y^{\prime }-y-2 x = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
3.272 |
|
|
\[
{}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.407 |
|
|
\[
{}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.346 |
|
|
\[
{}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
1.349 |
|
|
\[
{}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.723 |
|
|
\[
{}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
8.500 |
|
|
\[
{}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0
\] |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
2.833 |
|
|
\[
{}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.134 |
|
|
\[
{}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
7.550 |
|
|
\[
{}x y y^{\prime }+y^{2}+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.616 |
|
|
\[
{}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0
\] |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
3.384 |
|
|
\[
{}x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.138 |
|
|
\[
{}\left (x y+a \right ) y^{\prime }+b y = 0
\] |
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
0.960 |
|
|
\[
{}x \left (y+4\right ) y^{\prime }-y^{2}-2 y-2 x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.562 |
|
|
\[
{}x \left (a +y\right ) y^{\prime }+b y+c x = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
0.861 |
|
|
\[
{}\left (\left (x +y\right ) x +a \right ) y^{\prime }-y \left (x +y\right )-b = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.434 |
|
|
\[
{}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
4.438 |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a x = 0
\] |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
1.225 |
|
|
\[
{}2 x y y^{\prime }-y^{2}+a \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
4.194 |
|
|
\[
{}2 x y y^{\prime }+2 y^{2}+1 = 0
\] |
[_separable] |
✓ |
2.089 |
|
|
\[
{}x \left (x +2 y-1\right ) y^{\prime }-y \left (2 x +y+1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.393 |
|
|
\[
{}x \left (2 y-x -1\right ) y^{\prime }+y \left (2 x -y-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.398 |
|
|
\[
{}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.135 |
|
|
\[
{}x \left (3 y+2 x \right ) y^{\prime }+3 \left (x +y\right )^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
7.334 |
|
|
\[
{}\left (2+3 x \right ) \left (y-2 x -1\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0
\] |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
3.531 |
|
|
\[
{}\left (6 x y+x^{2}+3\right ) y^{\prime }+3 y^{2}+2 x y+2 x = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.338 |
|
|
\[
{}\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
5.079 |
|
|
\[
{}\left (B x y+A \,x^{2}+a x +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0
\] |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
7.591 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0
\] |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.226 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }+1-x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.848 |
|
|
\[
{}\left (x^{2} y-1\right ) y^{\prime }-8+8 x y^{2} = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.043 |
|
|
\[
{}x \left (x y-2\right ) y^{\prime }+y^{3} x^{2}+x y^{2}-2 y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.460 |
|
|
\[
{}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.894 |
|
|
\[
{}x^{2} \left (y-1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[_separable] |
✓ |
1.441 |
|
|
\[
{}x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
1.295 |
|
|
\[
{}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0
\] |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
2.082 |
|
|
\[
{}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0
\] |
[_Bernoulli] |
✓ |
2.052 |
|
|
\[
{}\left (2 x^{2} y+x \right ) y^{\prime }-y^{3} x^{2}+2 x y^{2}+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
2.390 |
|
|
\[
{}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.718 |
|
|
\[
{}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
32.902 |
|
|
\[
{}2 x^{3}+y^{\prime } y+3 x^{2} y^{2}+7 = 0
\] |
[_rational, _Bernoulli] |
✓ |
2.328 |
|
|
\[
{}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
2.143 |
|
|
\[
{}\left (x^{n \left (n +1\right )} y-1\right ) y^{\prime }+2 \left (n +1\right )^{2} x^{n -1} \left (x^{n^{2}} y^{2}-1\right ) = 0
\] |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
5.015 |
|
|
\[
{}\left (y-x \right ) \sqrt {x^{2}+1}\, y^{\prime }-a \sqrt {\left (1+y^{2}\right )^{3}} = 0
\] |
[‘x=_G(y,y’)‘] |
✗ |
569.649 |
|
|
\[
{}y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1 = 0
\] |
[_exact, _Bernoulli] |
✓ |
5.648 |
|
|
\[
{}f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right ) = 0
\] |
[_Bernoulli] |
✓ |
2.144 |
|
|
\[
{}\left (g_{1} \left (x \right ) y+g_{0} \left (x \right )\right ) y^{\prime }-f_{1} \left (x \right ) y-f_{2} \left (x \right ) y^{2}-f_{3} \left (x \right ) y^{3}-f_{0} \left (x \right ) = 0
\] |
[[_Abel, ‘2nd type‘, ‘class C‘]] |
✗ |
110.206 |
|
|
\[
{}\left (y^{2}-x \right ) y^{\prime }-y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.145 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.234 |
|
|
\[
{}\left (y^{2}+x^{2}\right ) y^{\prime }-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.896 |
|
|
\[
{}\left (y^{2}+x^{2}+a \right ) y^{\prime }+2 x y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.028 |
|
|
\[
{}\left (y^{2}+x^{2}+a \right ) y^{\prime }+2 x y+x^{2}+b = 0
\] |
[_exact, _rational] |
✓ |
1.231 |
|
|
\[
{}\left (y^{2}+x^{2}+x \right ) y^{\prime }-y = 0
\] |
[_rational] |
✓ |
1.123 |
|
|
\[
{}\left (y^{2}-x^{2}\right ) y^{\prime }+2 x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.405 |
|
|
\[
{}\left (y^{2}+x^{4}\right ) y^{\prime }-4 x^{3} y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.234 |
|
|
\[
{}\left (y^{2}+4 \sin \left (x \right )\right ) y^{\prime }-\cos \left (x \right ) = 0
\] |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.878 |
|
|
\[
{}\left (y^{2}+2 y+x \right ) y^{\prime }+\left (x +y\right )^{2} y^{2}+y \left (y+1\right ) = 0
\] |
[_rational] |
✗ |
3.807 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime }-a^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.353 |
|
|
\[
{}\left (y^{2}+2 x y-x^{2}\right ) y^{\prime }-y^{2}+2 x y+x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.714 |
|
|
\[
{}\left (y+3 x -1\right )^{2} y^{\prime }-\left (2 y-1\right ) \left (4 y+6 x -3\right ) = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
3.207 |
|
|
\[
{}3 \left (y^{2}-x^{2}\right ) y^{\prime }+2 y^{3}-6 x \left (x +1\right ) y-3 \,{\mathrm e}^{x} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.984 |
|
|
\[
{}\left (4 y^{2}+x^{2}\right ) y^{\prime }-x y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
3.045 |
|
|
\[
{}\left (4 y^{2}+2 x y+3 x^{2}\right ) y^{\prime }+y^{2}+6 x y+2 x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
7.824 |
|
|
\[
{}\left (2 y-3 x +1\right )^{2} y^{\prime }-\left (3 y-2 x -4\right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
36.395 |
|
|
\[
{}\left (2 y-4 x +1\right )^{2} y^{\prime }-\left (y-2 x \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
2.028 |
|
|
\[
{}\left (6 y^{2}-3 x^{2} y+1\right ) y^{\prime }-3 x y^{2}+x = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.398 |
|
|
\[
{}\left (6 y-x \right )^{2} y^{\prime }-6 y^{2}+2 x y+a = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.403 |
|
|
\[
{}\left (y^{2} a +2 b x y+c \,x^{2}\right ) y^{\prime }+b y^{2}+2 c x y+d \,x^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
374.393 |
|
|
\[
{}\left (b \left (\beta y+\alpha x \right )^{2}-\beta \left (a x +b y\right )\right ) y^{\prime }+a \left (\beta y+\alpha x \right )^{2}-\alpha \left (a x +b y\right ) = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.753 |
|
|
\[
{}\left (a y+b x +c \right )^{2} y^{\prime }+\left (\alpha y+\beta x +\gamma \right )^{2} = 0
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
3.431 |
|
|
\[
{}x \left (y^{2}-3 x \right ) y^{\prime }+2 y^{3}-5 x y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.007 |
|
|
\[
{}x \left (y^{2}+x^{2}-a \right ) y^{\prime }-y \left (y^{2}+x^{2}+a \right ) = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.236 |
|
|
\[
{}x \left (y^{2}+x y-x^{2}\right ) y^{\prime }-y^{3}+x y^{2}+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
84.797 |
|
|
\[
{}x \left (y^{2}+x^{2} y+x^{2}\right ) y^{\prime }-2 y^{3}-2 x^{2} y^{2}+x^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
2.958 |
|
|
\[
{}2 x \left (y^{2}+5 x^{2}\right ) y^{\prime }+y^{3}-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
22.463 |
|
|
\[
{}3 x y^{2} y^{\prime }+y^{3}-2 x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.280 |
|
|
\[
{}\left (3 x y^{2}-x^{2}\right ) y^{\prime }+y^{3}-2 x y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.027 |
|
|
\[
{}6 x y^{2} y^{\prime }+2 y^{3}+x = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.383 |
|
|
\[
{}\left (6 x y^{2}+x^{2}\right ) y^{\prime }-y \left (3 y^{2}-x \right ) = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.897 |
|
|
\[
{}\left (x^{2} y^{2}+x \right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.622 |
|
|
\[
{}\left (x y-1\right )^{2} x y^{\prime }+\left (x^{2} y^{2}+1\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.831 |
|
|
\[
{}\left (10 x^{3} y^{2}+x^{2} y+2 x \right ) y^{\prime }+5 y^{3} x^{2}+x y^{2} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.824 |
|
|
\[
{}\left (y^{3}-3 x \right ) y^{\prime }-3 y+x^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.175 |
|
|
\[
{}\left (y^{3}-x^{3}\right ) y^{\prime }-x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.316 |
|
|
\[
{}\left (y^{2}+x^{2}+a \right ) y y^{\prime }+\left (y^{2}+x^{2}-a \right ) x = 0
\] |
[_exact, _rational] |
✓ |
1.608 |
|
|
\[
{}2 y^{3} y^{\prime }+x y^{2} = 0
\] |
[_separable] |
✓ |
2.629 |
|
|
\[
{}\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x = 0
\] |
[_separable] |
✓ |
2.023 |
|
|
\[
{}\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
111.785 |
|
|
\[
{}\left (20 y^{3}-3 x y^{2}+6 x^{2} y+3 x^{3}\right ) y^{\prime }-y^{3}+6 x y^{2}+9 x^{2} y+4 x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
111.174 |
|