|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x \left (x^{2}+2 y^{2}\right ) y^{\prime } = \left (2 x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
110.914 |
|
|
\[
{}2 x \left (5 x^{2}+y^{2}\right ) y^{\prime } = x^{2} y-y^{3}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
105.948 |
|
|
\[
{}x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime } = \left (a x +2 y\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
442.716 |
|
|
\[
{}3 x y^{2} y^{\prime } = 2 x -y^{3}
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
11.348 |
|
|
\[
{}\left (1-4 x +3 x y^{2}\right ) y^{\prime } = \left (2-y^{2}\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.759 |
|
|
\[
{}x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
9.446 |
|
|
\[
{}3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3} = 0
\] |
[_rational] |
✓ |
3.017 |
|
|
\[
{}x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime } = 6 y^{3}
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
1.335 |
|
|
\[
{}6 x y^{2} y^{\prime }+x +2 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
9.662 |
|
|
\[
{}x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3} = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
7.743 |
|
|
\[
{}x \left (x^{2}-6 y^{2}\right ) y^{\prime } = 4 \left (x^{2}+3 y^{2}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
101.522 |
|
|
\[
{}x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
12.094 |
|
|
\[
{}x^{2} y^{2} y^{\prime }+1-x +x^{3} = 0
\] |
[_separable] |
✓ |
6.971 |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = x y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
4.927 |
|
|
\[
{}\left (1-x^{2} y^{2}\right ) y^{\prime } = \left (y x +1\right ) y^{2}
\] |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
6.589 |
|
|
\[
{}x \left (1+x y^{2}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
15.353 |
|
|
\[
{}x \left (1+x y^{2}\right ) y^{\prime } = \left (2-3 x y^{2}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
24.150 |
|
|
\[
{}x^{2} \left (a +y\right )^{2} y^{\prime } = \left (x^{2}+1\right ) \left (y^{2}+a^{2}\right )
\] |
[_separable] |
✓ |
3.990 |
|
|
\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right ) = 0
\] |
[_separable] |
✓ |
42.809 |
|
|
\[
{}\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2} = 0
\] |
[_separable] |
✓ |
7.360 |
|
|
\[
{}\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime } = \left (6+3 y x -4 y^{3}\right ) x
\] |
[_exact, _rational] |
✓ |
3.312 |
|
|
\[
{}x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y = 0
\] |
[_exact, _rational] |
✓ |
3.256 |
|
|
\[
{}x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y = 0
\] |
[_separable] |
✓ |
11.385 |
|
|
\[
{}x \left (1-y x \right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
9.188 |
|
|
\[
{}\left (1-x^{4} y^{2}\right ) y^{\prime } = x^{3} y^{3}
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
16.896 |
|
|
\[
{}\left (3 x -y^{3}\right ) y^{\prime } = x^{2}-3 y
\] |
[_exact, _rational] |
✓ |
6.366 |
|
|
\[
{}\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
64.339 |
|
|
\[
{}\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
924.457 |
|
|
\[
{}\left (x -x^{2} y-y^{3}\right ) y^{\prime } = x^{3}-y+x y^{2}
\] |
[_exact, _rational] |
✓ |
2.575 |
|
|
\[
{}\left (a^{2} x +\left (x^{2}-y^{2}\right ) y\right ) y^{\prime }+x \left (x^{2}-y^{2}\right ) = a^{2} y
\] |
[_rational] |
✓ |
3.621 |
|
|
\[
{}\left (a +x^{2}+y^{2}\right ) y y^{\prime } = x \left (a -x^{2}-y^{2}\right )
\] |
[_exact, _rational] |
✓ |
7.403 |
|
|
\[
{}\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
150.886 |
|
|
\[
{}\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right ) = 0
\] |
[_rational] |
✗ |
1.384 |
|
|
\[
{}2 y^{3} y^{\prime } = x^{3}-x y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
71.082 |
|
|
\[
{}y \left (1+2 y^{2}\right ) y^{\prime } = x \left (2 x^{2}+1\right )
\] |
[_separable] |
✓ |
9.724 |
|
|
\[
{}\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
140.658 |
|
|
\[
{}\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
224.812 |
|
|
\[
{}\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3} = 0
\] |
[_rational] |
✗ |
1.397 |
|
|
\[
{}\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3} = 0
\] |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
170.764 |
|
|
\[
{}\left (x^{3}+a y^{3}\right ) y^{\prime } = x^{2} y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
46.563 |
|
|
\[
{}x y^{3} y^{\prime } = \left (-x^{2}+1\right ) \left (1+y^{2}\right )
\] |
[_separable] |
✓ |
10.303 |
|
|
\[
{}x \left (x -y^{3}\right ) y^{\prime } = \left (3 x +y^{3}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
14.672 |
|
|
\[
{}x \left (2 x^{3}+y^{3}\right ) y^{\prime } = \left (2 x^{3}-x^{2} y+y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
18.313 |
|
|
\[
{}x \left (2 x^{3}-y^{3}\right ) y^{\prime } = \left (x^{3}-2 y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
48.306 |
|
|
\[
{}x \left (x^{3}+3 x^{2} y+y^{3}\right ) y^{\prime } = \left (3 x^{2}+y^{2}\right ) y^{2}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
26.807 |
|
|
\[
{}x \left (x^{3}-2 y^{3}\right ) y^{\prime } = \left (2 x^{3}-y^{3}\right ) y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
22.589 |
|
|
\[
{}x \left (x^{4}-2 y^{3}\right ) y^{\prime }+\left (2 x^{4}+y^{3}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
27.250 |
|
|
\[
{}x \left (x +y+2 y^{3}\right ) y^{\prime } = \left (x -y\right ) y
\] |
[_rational] |
✓ |
4.569 |
|
|
\[
{}\left (5 x -y-7 x y^{3}\right ) y^{\prime }+5 y-y^{4} = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.496 |
|
|
\[
{}x \left (1-2 x y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y\right ) y = 0
\] |
[_rational] |
✓ |
7.532 |
|
|
\[
{}x \left (2-x y^{2}-2 x y^{3}\right ) y^{\prime }+1+2 y = 0
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
4.294 |
|
|
\[
{}\left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime } = x \left (1+5 y^{4}\right )
\] |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
3.110 |
|
|
\[
{}x \left (a +b x y^{3}\right ) y^{\prime }+\left (a +c \,x^{3} y\right ) y = 0
\] |
[_rational] |
✓ |
9.026 |
|
|
\[
{}x \left (1-2 x^{2} y^{3}\right ) y^{\prime }+\left (1-2 x^{3} y^{2}\right ) y = 0
\] |
[_rational] |
✓ |
2.802 |
|
|
\[
{}x \left (1-y x \right ) \left (1-x^{2} y^{2}\right ) y^{\prime }+\left (y x +1\right ) \left (1+x^{2} y^{2}\right ) y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
8.875 |
|
|
\[
{}\left (x^{2}-y^{4}\right ) y^{\prime } = y x
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
32.625 |
|
|
\[
{}\left (x^{3}-y^{4}\right ) y^{\prime } = 3 x^{2} y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
15.151 |
|
|
\[
{}\left (a^{2} x^{2}+\left (x^{2}+y^{2}\right )^{2}\right ) y^{\prime } = a^{2} x y
\] |
[_rational] |
✓ |
15.641 |
|
|
\[
{}2 \left (x -y^{4}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
32.171 |
|
|
\[
{}\left (4 x -x y^{3}-2 y^{4}\right ) y^{\prime } = \left (2+y^{3}\right ) y
\] |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
6.120 |
|
|
\[
{}\left (a \,x^{3}+\left (a x +b y\right )^{3}\right ) y y^{\prime }+x \left (\left (a x +b y\right )^{3}+b y^{3}\right ) = 0
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
98.832 |
|
|
\[
{}\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+\left (1+y^{4}\right ) y = 0
\] |
[_rational] |
✗ |
1.367 |
|
|
\[
{}2 x \left (x^{3}+y^{4}\right ) y^{\prime } = \left (x^{3}+2 y^{4}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
36.226 |
|
|
\[
{}x \left (1-x^{2} y^{4}\right ) y^{\prime }+y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
37.668 |
|
|
\[
{}\left (x^{2}-y^{5}\right ) y^{\prime } = 2 y x
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
16.797 |
|
|
\[
{}x \left (x^{3}+y^{5}\right ) y^{\prime } = \left (x^{3}-y^{5}\right ) y
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
14.106 |
|
|
\[
{}x^{3} \left (1+5 x^{3} y^{7}\right ) y^{\prime }+\left (3 x^{5} y^{5}-1\right ) y^{3} = 0
\] |
[_rational] |
✓ |
7.533 |
|
|
\[
{}\left (1+a \left (x +y\right )\right )^{n} y^{\prime }+a \left (x +y\right )^{n} = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
18.178 |
|
|
\[
{}x \left (a +x y^{n}\right ) y^{\prime }+b y = 0
\] |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
6.521 |
|
|
\[
{}f \left (x \right ) y^{m} y^{\prime }+g \left (x \right ) y^{m +1}+h \left (x \right ) y^{n} = 0
\] |
[_Bernoulli] |
✗ |
2.008 |
|
|
\[
{}y^{\prime } \sqrt {b^{2}+y^{2}} = \sqrt {a^{2}+x^{2}}
\] |
[_separable] |
✓ |
5.191 |
|
|
\[
{}y^{\prime } \sqrt {-y^{2}+b^{2}} = \sqrt {a^{2}-x^{2}}
\] |
[_separable] |
✓ |
15.339 |
|
|
\[
{}y^{\prime } \sqrt {y} = \sqrt {x}
\] |
[_separable] |
✓ |
109.036 |
|
|
\[
{}\left (1+\sqrt {x +y}\right ) y^{\prime }+1 = 0
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
12.037 |
|
|
\[
{}y^{\prime } \sqrt {y x}+x -y = \sqrt {y x}
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
64.503 |
|
|
\[
{}\left (x -2 \sqrt {y x}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
282.022 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
108.478 |
|
|
\[
{}\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime } = 1+y^{2}
\] |
[_separable] |
✓ |
69.133 |
|
|
\[
{}\left (x -\sqrt {x^{2}+y^{2}}\right ) y^{\prime } = y
\] |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
182.233 |
|
|
\[
{}x \left (1-\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = y
\] |
[‘y=_G(x,y’)‘] |
✗ |
1.649 |
|
|
\[
{}x \left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }+y \sqrt {x^{2}+y^{2}} = 0
\] |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
284.924 |
|
|
\[
{}x y \left (x +\sqrt {x^{2}-y^{2}}\right ) y^{\prime } = x y^{2}-\left (x^{2}-y^{2}\right )^{{3}/{2}}
\] |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
202.880 |
|
|
\[
{}\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime } = x \left (x^{2}+y^{2}\right )+y \sqrt {1+x^{2}+y^{2}}
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
123.090 |
|
|
\[
{}y^{\prime } \cos \left (y\right ) \left (\cos \left (y\right )-\sin \left (A \right ) \sin \left (x \right )\right )+\cos \left (x \right ) \left (\cos \left (x \right )-\sin \left (A \right ) \sin \left (y\right )\right ) = 0
\] |
unknown |
✓ |
203.183 |
|
|
\[
{}\left (a \cos \left (b x +a y\right )-b \sin \left (a x +b y\right )\right ) y^{\prime }+b \cos \left (b x +a y\right )-a \sin \left (a x +b y\right ) = 0
\] |
[_exact] |
✓ |
69.570 |
|
|
\[
{}\left (x +\cos \left (x \right ) \sec \left (y\right )\right ) y^{\prime }+\tan \left (y\right )-y \sin \left (x \right ) \sec \left (y\right ) = 0
\] |
[NONE] |
✓ |
165.505 |
|
|
\[
{}\left (1+\left (x +y\right ) \tan \left (y\right )\right ) y^{\prime }+1 = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
64.622 |
|
|
\[
{}x \left (x -y \tan \left (\frac {y}{x}\right )\right ) y^{\prime }+\left (x +y \tan \left (\frac {y}{x}\right )\right ) y = 0
\] |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
105.504 |
|
|
\[
{}\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y} = 0
\] |
[_exact] |
✓ |
93.881 |
|
|
\[
{}\left (1-2 x -\ln \left (y\right )\right ) y^{\prime }+2 y = 0
\] |
[[_1st_order, _with_linear_symmetries]] |
✓ |
25.061 |
|
|
\[
{}\left (\sinh \left (x \right )+x \cosh \left (y\right )\right ) y^{\prime }+y \cosh \left (x \right )+\sinh \left (y\right ) = 0
\] |
[_exact] |
✓ |
210.702 |
|
|
\[
{}y^{\prime } \left (1+\sinh \left (x \right )\right ) \sinh \left (y\right )+\cosh \left (x \right ) \left (\cosh \left (y\right )-1\right ) = 0
\] |
[_separable] |
✓ |
141.960 |
|
|
\[
{}{y^{\prime }}^{2} = a \,x^{n}
\] |
[_quadrature] |
✓ |
1.073 |
|
|
\[
{}{y^{\prime }}^{2} = y
\] |
[_quadrature] |
✓ |
3.152 |
|
|
\[
{}{y^{\prime }}^{2} = x -y
\] |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
14.211 |
|
|
\[
{}{y^{\prime }}^{2} = y+x^{2}
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
200.229 |
|
|
\[
{}{y^{\prime }}^{2}+x^{2} = 4 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
264.116 |
|
|
\[
{}{y^{\prime }}^{2}+3 x^{2} = 8 y
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
258.399 |
|
|
\[
{}{y^{\prime }}^{2}+a \,x^{2}+b y = 0
\] |
[[_homogeneous, ‘class G‘]] |
✓ |
250.158 |
|
|
\[
{}{y^{\prime }}^{2} = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.499 |
|