# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
\[ {}x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x = 0 \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
3.405 |
|
\[ {}2 x \left (-1+x \right ) y^{\prime }+\left (-1+x \right ) y^{2}-x = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.408 |
|
\[ {}3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2} = 0 \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.614 |
|
\[ {}3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3 = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.335 |
|
\[ {}\left (x a +b \right )^{2} y^{\prime }+\left (x a +b \right ) y^{3}+c y^{2} = 0 \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
6.46 |
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{4} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.056 |
|
\[ {}x^{3} y^{\prime }-y^{2}-x^{2} y = 0 \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.181 |
|
\[ {}x^{3} y^{\prime }-x^{4} y^{2}+x^{2} y+20 = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.99 |
|
\[ {}x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3 = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.912 |
|
\[ {}x \left (x^{2}+1\right ) y^{\prime }+x^{2} y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.967 |
|
\[ {}x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3} = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.795 |
|
\[ {}x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.658 |
|
\[ {}x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (-2+x \right ) y = 0 \] |
riccati, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.302 |
|
\[ {}2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3 = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
2.309 |
|
\[ {}3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
3.339 |
|
\[ {}\left (x^{2} a +b x +c \right ) \left (-y+x y^{\prime }\right )-y^{2}+x^{2} = 0 \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
2.892 |
|
\[ {}x^{4} \left (y^{\prime }+y^{2}\right )+a = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
2.418 |
|
\[ {}x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.973 |
|
\[ {}\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.318 |
|
\[ {}\left (x^{2} a +b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, _Riccati] |
✓ |
✓ |
5.824 |
|
\[ {}x^{7} y^{\prime }+2 \left (x^{2}+1\right ) y^{3}+5 x^{3} y^{2} = 0 \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
61.957 |
|
\[ {}x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
2.357 |
|
\[ {}x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
5.237 |
|
\[ {}x^{2 n +1} y^{\prime }-a y^{3}-b \,x^{3 n} = 0 \] |
abelFirstKind, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
1.615 |
|
\[ {}x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (1+m \right )} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
2.809 |
|
\[ {}\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
15.137 |
|
\[ {}\sqrt {-x^{2}+1}\, y^{\prime }-y \sqrt {y^{2}-1} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.783 |
|
\[ {}\sqrt {a^{2}+x^{2}}\, y^{\prime }+y-\sqrt {a^{2}+x^{2}}+x = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.701 |
|
\[ {}x y^{\prime } \ln \left (x \right )+y-a x \left (1+\ln \left (x \right )\right ) = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.624 |
|
\[ {}x y^{\prime } \ln \left (x \right )-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3} = 0 \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.189 |
|
\[ {}\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4 = 0 \] |
riccati |
[_Riccati] |
✓ |
✓ |
15.024 |
|
\[ {}\cos \left (x \right ) y^{\prime }+y+\left (\sin \left (x \right )+1\right ) \cos \left (x \right ) = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.306 |
|
\[ {}\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right ) = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
47.638 |
|
\[ {}\sin \left (x \right ) \cos \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.431 |
|
\[ {}\sin \left (2 x \right ) y^{\prime }+\sin \left (2 y\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
27.957 |
|
\[ {}\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right ) = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.359 |
|
\[ {}2 f \left (x \right ) y^{\prime }+2 y^{2} f \left (x \right )-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2} = 0 \] |
riccati |
[_Riccati] |
✓ |
✓ |
0.951 |
|
\[ {}f \left (x \right ) y^{\prime }+g \left (x \right ) s \left (y\right )+h \left (x \right ) = 0 \] |
unknown |
[NONE] |
❇ |
N/A |
0.99 |
|
\[ {}y y^{\prime }+y+x^{3} = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
0.529 |
|
\[ {}y y^{\prime }+a y+x = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
22.648 |
|
\[ {}y y^{\prime }+a y+\frac {\left (a^{2}-1\right ) x}{4}+b \,x^{n} = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
1.325 |
|
\[ {}y y^{\prime }+a y+b \,{\mathrm e}^{x}-2 a = 0 \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
1.085 |
|
\[ {}y y^{\prime }+y^{2}+4 \left (1+x \right ) x = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.217 |
|
\[ {}y y^{\prime }+a y^{2}-b \cos \left (x +c \right ) = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.21 |
|
\[ {}y y^{\prime }-\sqrt {a y^{2}+b} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.638 |
|
\[ {}y y^{\prime }+x y^{2}-4 x = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.973 |
|
\[ {}y y^{\prime }-x \,{\mathrm e}^{\frac {x}{y}} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.521 |
|
\[ {}y y^{\prime }+f \left (x^{2}+y^{2}\right ) g \left (x \right )+x = 0 \] |
unknown |
[NONE] |
✗ |
N/A |
2.21 |
|
\[ {}\left (y+1\right ) y^{\prime }-y-x = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
12.486 |
|
\[ {}\left (x +y-1\right ) y^{\prime }-y+2 x +3 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.851 |
|
\[ {}\left (y+2 x -2\right ) y^{\prime }-y+x +1 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.328 |
|
\[ {}\left (y-2 x +1\right ) y^{\prime }+y+x = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.267 |
|
\[ {}\left (-x^{2}+y\right ) y^{\prime }-x = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.368 |
|
\[ {}\left (-x^{2}+y\right ) y^{\prime }+4 x y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.253 |
|
\[ {}\left (y+g \left (x \right )\right ) y^{\prime }-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right ) = 0 \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
9.226 |
|
\[ {}2 y y^{\prime }-x y^{2}-x^{3} = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.375 |
|
\[ {}\left (2 y+x +1\right ) y^{\prime }-2 y-x +1 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.27 |
|
\[ {}\left (2 y+x +7\right ) y^{\prime }-y+2 x +4 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.214 |
|
\[ {}\left (2 y-x \right ) y^{\prime }-y-2 x = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.146 |
|
\[ {}\left (2 y-6 x \right ) y^{\prime }-y+3 x +2 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.451 |
|
\[ {}\left (4 y+2 x +3\right ) y^{\prime }-2 y-x -1 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.293 |
|
\[ {}\left (4 y-2 x -3\right ) y^{\prime }+2 y-x -1 = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.315 |
|
\[ {}\left (4 y-3 x -5\right ) y^{\prime }-3 y+7 x +2 = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.281 |
|
\[ {}\left (4 y+11 x -11\right ) y^{\prime }-25 y-8 x +62 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.253 |
|
\[ {}\left (12 y-5 x -8\right ) y^{\prime }-5 y+2 x +3 = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.935 |
|
\[ {}a y y^{\prime }+b y^{2}+f \left (x \right ) = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.867 |
|
\[ {}\left (a y+b x +c \right ) y^{\prime }+\alpha y+\beta x +\gamma = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.463 |
|
\[ {}x y y^{\prime }+y^{2}+x^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.885 |
|
\[ {}x y y^{\prime }-y^{2}+a \,x^{3} \cos \left (x \right ) = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.794 |
|
\[ {}x y y^{\prime }-y^{2}+x y+x^{3}-2 x^{2} = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.738 |
|
\[ {}\left (x y+a \right ) y^{\prime }+b y = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, _with_exponential_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.537 |
|
\[ {}x \left (y+4\right ) y^{\prime }-y^{2}-2 y-2 x = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.61 |
|
\[ {}x \left (y+a \right ) y^{\prime }+b y+c x = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.77 |
|
\[ {}\left (x \left (x +y\right )+a \right ) y^{\prime }-y \left (x +y\right )-b = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.793 |
|
\[ {}\left (x y-x^{2}\right ) y^{\prime }+y^{2}-3 x y-2 x^{2} = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.605 |
|
\[ {}2 x y y^{\prime }-y^{2}+x a = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.388 |
|
\[ {}2 x y y^{\prime }-y^{2}+x^{2} a = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.811 |
|
\[ {}2 x y y^{\prime }+2 y^{2}+1 = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.362 |
|
\[ {}x \left (2 y+x -1\right ) y^{\prime }-y \left (y+2 x +1\right ) = 0 \] |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.121 |
|
\[ {}x \left (2 y-x -1\right ) y^{\prime }+y \left (2 x -y-1\right ) = 0 \] |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.125 |
|
\[ {}\left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.468 |
|
\[ {}x \left (3 y+2 x \right ) y^{\prime }+3 \left (x +y\right )^{2} = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.754 |
|
\[ {}\left (3 x +2\right ) \left (-1-2 x +y\right ) y^{\prime }-y^{2}+x y-7 x^{2}-9 x -3 = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.573 |
|
\[ {}\left (6 x y+x^{2}+3\right ) y^{\prime }+3 y^{2}+2 x y+2 x = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.834 |
|
\[ {}\left (a x y+b \,x^{n}\right ) y^{\prime }+\alpha y^{3}+\beta y^{2} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
10.773 |
|
\[ {}\left (B x y+A \,x^{2}+x a +b y+c \right ) y^{\prime }-B g \left (x \right )^{2}+A x y+\alpha x +\beta y+\gamma = 0 \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
6.216 |
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }+x y^{2}-1 = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.626 |
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }-x y^{2}+1 = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.338 |
|
\[ {}\left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8 = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.757 |
|
\[ {}x \left (x y-2\right ) y^{\prime }+x^{2} y^{3}+x y^{2}-2 y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.533 |
|
\[ {}x \left (x y-3\right ) y^{\prime }+x y^{2}-y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.989 |
|
\[ {}x^{2} \left (y-1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.733 |
|
\[ {}x \left (x y+x^{4}-1\right ) y^{\prime }-y \left (x y-x^{4}-1\right ) = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
N/A |
1.035 |
|
\[ {}2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
2.801 |
|
\[ {}2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}} = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.458 |
|
\[ {}\left (2 x^{2} y+x \right ) y^{\prime }-x^{2} y^{3}+2 x y^{2}+y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
1.589 |
|
\[ {}\left (2 x^{2} y-x \right ) y^{\prime }-2 x y^{2}-y = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.831 |
|
\[ {}\left (2 x^{2} y-x^{3}\right ) y^{\prime }+y^{3}-4 x y^{2}+2 x^{3} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.803 |
|
\[ {}2 x^{3}+y y^{\prime }+3 x^{2} y^{2}+7 = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
3.064 |
|
\[ {}2 x \left (x^{3} y+1\right ) y^{\prime }+\left (3 x^{3} y-1\right ) y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.406 |
|
|
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|
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