|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.219 |
|
|
\[ {}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.759 |
|
|
\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.18 |
|
|
\[ {}y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.964 |
|
|
\[ {}y^{\prime } = \frac {a y+b}{d +c y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.633 |
|
|
\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.151 |
|
|
\[ {}y^{\prime } = -\frac {4 x +3 y}{y+2 x} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.331 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{x -y} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.486 |
|
|
\[ {}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.265 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.518 |
|
|
\[ {}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.69 |
|
|
\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.693 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.746 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.372 |
|
|
\[ {}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
168.757 |
|
|
\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{1+y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.37 |
|
|
\[ {}y^{\prime } = -\frac {4 t}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = 2 t y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{3}+y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime } = t \left (3-y\right ) y \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = y \left (3-t y\right ) \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = -y \left (3-t y\right ) \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.822 |
|
|
\[ {}y^{\prime } = t -1-y^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.582 |
|
|
\[ {}y^{\prime } = a y+b y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.938 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.542 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{-y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.531 |
|
|
\[ {}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
3.049 |
|
|
\[ {}y^{\prime } = -k \left (-1+y\right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.24 |
|
|
\[ {}y^{\prime } = y^{2} \left (y^{2}-1\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.505 |
|
|
\[ {}y^{\prime } = y \left (1-y^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.153 |
|
|
\[ {}y^{\prime } = -b \sqrt {y}+a y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.737 |
|
|
\[ {}y^{\prime } = y^{2} \left (4-y^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.51 |
|
|
\[ {}y^{\prime } = \left (1-y\right )^{2} y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.559 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.759 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.393 |
|
|
\[ {}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
18.126 |
|
|
\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime } = \frac {-x a -b y}{b x +c y} \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.531 |
|
|
\[ {}y^{\prime } = \frac {-x a +b y}{b x -c y} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.492 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
10.509 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \] |
unknown |
[‘x=_G(y,y’)‘] |
❇ |
N/A |
7.641 |
|
|
\[ {}2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
9.246 |
|
|
\[ {}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.185 |
|
|
\[ {}x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.007 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
8.075 |
|
|
\[ {}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.512 |
|
|
\[ {}y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.997 |
|
|
\[ {}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
3.155 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{2 x}+y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.841 |
|
|
\[ {}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0 \] |
exact, differentialType |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.234 |
|
|
\[ {}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
2.399 |
|
|
\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.892 |
|
|
\[ {}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_rational] |
✓ |
✓ |
2.105 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_rational] |
✓ |
✓ |
14.87 |
|
|
\[ {}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.201 |
|
|
\[ {}y^{\prime } = \frac {x^{3}-2 y}{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.846 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.089 |
|
|
\[ {}y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}} \] |
exact, differentialType |
[_rational] |
✓ |
✓ |
280.432 |
|
|
\[ {}y^{\prime } = 3-6 x +y-2 x y \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.21 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y} \] |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.851 |
|
|
\[ {}x y+x y^{\prime } = 1-y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.539 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
89.541 |
|
|
\[ {}2 y+x y^{\prime } = \frac {\sin \left (x \right )}{x} \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y} \] |
exact, differentialType |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.277 |
|
|
\[ {}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{-2+y} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact] |
✓ |
✓ |
3.525 |
|
|
\[ {}y+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.109 |
|
|
\[ {}x +y+\left (2 y+x \right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.832 |
|
|
\[ {}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-{\mathrm e}^{x} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.78 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \] |
exactWithIntegrationFactor |
[NONE] |
✓ |
✓ |
48.562 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x}+3 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.88 |
|
|
\[ {}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.011 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \] |
exact |
[_rational] |
✓ |
✓ |
2.016 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.915 |
|
|
\[ {}\frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0 \] |
exact |
[_rational] |
✓ |
✓ |
2.35 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
67.306 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = {\mathrm e}^{2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.082 |
|
|
\[ {}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.416 |
|
|
\[ {}\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
2.711 |
|
|
\[ {}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime } = \frac {x}{x^{2}+y+y^{3}} \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.819 |
|
|
\[ {}3 t +2 y = -t y^{\prime } \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.519 |
|
|
\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.812 |
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\[ {}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.122 |
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|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.315 |
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