|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left (3 x^{2}-y^{2}\right ) y^{\prime } = 2 x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
4.009 |
|
|
\[
{}\left (x^{4}+y^{2}\right ) y^{\prime } = 4 x^{3} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.276 |
|
|
\[
{}y \left (y+1\right ) y^{\prime } = \left (x +1\right ) x
\] |
[_separable] |
✓ |
1.387 |
|
|
\[
{}\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2} = 0
\] |
[_rational] |
✗ |
3.712 |
|
|
\[
{}\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.174 |
|
|
\[
{}\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.148 |
|
|
\[
{}\left (1+y+x y+y^{2}\right ) y^{\prime }+1+y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.299 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
3.371 |
|
|
\[
{}\left (x -y\right )^{2} y^{\prime } = a^{2}
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
2.345 |
|
|
\[
{}\left (x^{2}+2 x y-y^{2}\right ) y^{\prime }+x^{2}-2 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.826 |
|
|
\[
{}\left (x +y\right )^{2} y^{\prime } = x^{2}-2 x y+5 y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.150 |
|
|
\[
{}\left (a +b +x +y\right )^{2} y^{\prime } = 2 \left (a +y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
2.007 |
|
|
\[
{}\left (2 x^{2}+4 x y-y^{2}\right ) y^{\prime } = x^{2}-4 x y-2 y^{2}
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
4.562 |
|
|
\[
{}\left (3 x +y\right )^{2} y^{\prime } = 4 \left (3 x +2 y\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
17.880 |
|
|
\[
{}\left (1-3 x -y\right )^{2} y^{\prime } = \left (1-2 y\right ) \left (3-6 x -4 y\right )
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
3.237 |
|
|
\[
{}\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime } = y^{3} \csc \left (x \right ) \sec \left (x \right )
\] |
[‘y=_G(x,y’)‘] |
✗ |
58.056 |
|
|
\[
{}3 y^{2} y^{\prime } = 1+x +a y^{3}
\] |
[_rational, _Bernoulli] |
✓ |
1.688 |
|
|
\[
{}\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 x y = 0
\] |
[_exact, _rational] |
✓ |
1.112 |
|
|
\[
{}\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
7.506 |
|
|
\[
{}3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 x y \left (x +1\right )-2 y^{3} = 0
\] |
[‘y=_G(x,y’)‘] |
✓ |
1.911 |
|
|
\[
{}\left (3 x^{2}+2 x y+4 y^{2}\right ) y^{\prime }+2 x^{2}+6 x y+y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
7.796 |
|
|
\[
{}\left (1-3 x +2 y\right )^{2} y^{\prime } = \left (4+2 x -3 y\right )^{2}
\] |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
36.577 |
|
|
\[
{}\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2} = 0
\] |
[_exact, _rational] |
✓ |
1.471 |
|
|
\[
{}\left (x -6 y\right )^{2} y^{\prime }+a +2 x y-6 y^{2} = 0
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
1.389 |
|
|
\[
{}\left (x^{2}+y^{2} a \right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
2.731 |
|
|
\[
{}\left (x^{2}+x y+y^{2} a \right ) y^{\prime } = a \,x^{2}+x y+y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
22.418 |
|
|
\[
{}\left (a \,x^{2}+2 x y-y^{2} a \right ) y^{\prime }+x^{2}-2 a x y-y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
9.435 |
|
|
\[
{}\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
293.157 |
|
|
\[
{}x \left (1-y^{2}\right ) y^{\prime } = \left (x^{2}+1\right ) y
\] |
[_separable] |
✓ |
1.672 |
|
|
\[
{}x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.188 |
|
|
\[
{}x \left (y^{2}+x^{2}\right ) y^{\prime } = \left (x^{2}+x^{4}+y^{2}\right ) y
\] |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
1.550 |
|
|
\[
{}x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.194 |
|
|
\[
{}x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
4.155 |
|
|
\[
{}x \left (2 x^{2}+y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
15.579 |
|
|
\[
{}\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y = 0
\] |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
1.757 |
|
|
\[
{}x \left (a +y\right )^{2} y^{\prime } = b y^{2}
\] |
[_separable] |
✓ |
1.484 |
|
|
\[
{}x \left (x^{2}-x y+y^{2}\right ) y^{\prime }+\left (y^{2}+x y+x^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
52.489 |
|
|
\[
{}x \left (x^{2}-x y-y^{2}\right ) y^{\prime } = \left (x^{2}+x y-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
68.483 |
|
|
\[
{}x \left (x^{2}+a x y+y^{2}\right ) y^{\prime } = \left (x^{2}+b x y+y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
176.970 |
|
|
\[
{}x \left (-2 y^{2}+x^{2}\right ) y^{\prime } = \left (2 x^{2}-y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
23.350 |
|
|
\[
{}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
26.695 |
|
|
\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
22.674 |
|
|
\[
{}x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime } = \left (a x +2 y\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
298.046 |
|
|
\[
{}3 x y^{2} y^{\prime } = 2 x -y^{3}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.297 |
|
|
\[
{}\left (1-4 x +3 x y^{2}\right ) y^{\prime } = \left (2-y^{2}\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.601 |
|
|
\[
{}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
2.004 |
|
|
\[
{}3 x \left (y^{2}+x \right ) y^{\prime }+x^{3}-3 x y-2 y^{3} = 0
\] |
[_rational] |
✓ |
1.539 |
|
|
\[
{}x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime } = 6 y^{3}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.260 |
|
|
\[
{}6 x y^{2} y^{\prime }+x +2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
2.438 |
|
|
\[
{}x \left (x +6 y^{2}\right ) y^{\prime }+x y-3 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.858 |
|
|
\[
{}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
28.779 |
|
|
\[
{}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.249 |
|
|
\[
{}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0
\] |
[_separable] |
✓ |
1.993 |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = x y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.760 |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (x y+1\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
1.469 |
|
|
\[
{}x \left (x y^{2}+1\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
3.535 |
|
|
\[
{}x \left (x y^{2}+1\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
5.036 |
|
|
\[
{}x^{2} \left (a +y\right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right )
\] |
[_separable] |
✓ |
1.345 |
|
|
\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
23.106 |
|
|
\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0
\] |
[_separable] |
✓ |
2.019 |
|
|
\[
{}\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime } = \left (6+3 x y-4 y^{3}\right ) x
\] |
[_exact, _rational] |
✓ |
1.552 |
|
|
\[
{}x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0
\] |
[_exact, _rational] |
✓ |
2.079 |
|
|
\[
{}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
2.396 |
|
|
\[
{}x \left (1-x y\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.812 |
|
|
\[
{}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.697 |
|
|
\[
{}\left (3 x -y^{3}\right ) y^{\prime } = x^{2}-3 y
\] |
[_exact, _rational] |
✓ |
1.236 |
|
|
\[
{}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.713 |
|
|
\[
{}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
331.203 |
|
|
\[
{}\left (x -x^{2} y-y^{3}\right ) y^{\prime } = x^{3}-y+x y^{2}
\] |
[_exact, _rational] |
✓ |
1.631 |
|
|
\[
{}\left (a^{2} x +\left (x^{2}-y^{2}\right ) y\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = a^{2} y
\] |
[_rational] |
✓ |
1.701 |
|
|
\[
{}\left (a +x^{2}+y^{2}\right ) y y^{\prime } = x \left (a -x^{2}-y^{2}\right )
\] |
[_exact, _rational] |
✓ |
1.618 |
|
|
\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
63.525 |
|
|
\[
{}\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right ) = 0
\] |
[_rational] |
✗ |
2.780 |
|
|
\[
{}2 y^{3} y^{\prime } = x^{3}-x y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
16.878 |
|
|
\[
{}y \left (1+2 y^{2}\right ) y^{\prime } = x \left (2 x^{2}+1\right )
\] |
[_separable] |
✓ |
2.042 |
|
|
\[
{}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
80.948 |
|
|
\[
{}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
105.450 |
|
|
\[
{}\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0
\] |
[_rational] |
✗ |
2.763 |
|
|
\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
112.334 |
|
|
\[
{}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
10.284 |
|
|
\[
{}x y^{3} y^{\prime } = \left (-x^{2}+1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
2.015 |
|
|
\[
{}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.783 |
|
|
\[
{}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
5.188 |
|
|
\[
{}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
12.769 |
|
|
\[
{}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.349 |
|
|
\[
{}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
6.359 |
|
|
\[
{}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.244 |
|
|
\[
{}x \left (x +y+2 y^{3}\right ) y^{\prime } = \left (x -y\right ) y
\] |
[_rational] |
✓ |
1.527 |
|
|
\[
{}\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.093 |
|
|
\[
{}x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y = 0
\] |
[_rational] |
✓ |
1.521 |
|
|
\[
{}x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.591 |
|
|
\[
{}\left (2-10 y^{3} x^{2}+3 y^{2}\right ) y^{\prime } = x \left (1+5 y^{4}\right )
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
1.494 |
|
|
\[
{}x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y = 0
\] |
[_rational] |
✓ |
1.697 |
|
|
\[
{}x \left (1-2 y^{3} x^{2}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y = 0
\] |
[_rational] |
✓ |
1.436 |
|
|
\[
{}x \left (1-x y\right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (x y+1\right ) \left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
1.844 |
|
|
\[
{}\left (x^{2}-y^{4}\right ) y^{\prime } = x y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.134 |
|
|
\[
{}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
2.784 |
|
|
\[
{}\left (a^{2} x^{2}+\left (y^{2}+x^{2}\right )^{2}\right ) y^{\prime } = a^{2} x y
\] |
[_rational] |
✓ |
3.829 |
|
|
\[
{}2 \left (x -y^{4}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.067 |
|
|
\[
{}\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime } = \left (2+y^{3}\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
2.848 |
|