|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{3} y^{\prime } = x^{4}+y^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.602 |
|
|
\[ {}x^{3} y^{\prime } = y \left (y+x^{2}\right ) \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.691 |
|
|
\[ {}x^{3} y^{\prime } = x^{2} \left (y-1\right )+y^{2} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.47 |
|
|
\[ {}x^{3} y^{\prime } = \left (1+x \right ) y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.538 |
|
|
\[ {}x^{3} y^{\prime }+20+x^{2} y \left (1-x^{2} y\right ) = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.165 |
|
|
\[ {}x^{3} y^{\prime }+3+\left (3-2 x \right ) x^{2} y-x^{6} y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.024 |
|
|
\[ {}x^{3} y^{\prime } = \left (2 x^{2}+y^{2}\right ) y \] |
bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.748 |
|
|
\[ {}x^{3} y^{\prime } = \cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
1.839 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = x^{2} a +y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.743 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = x^{2} a +y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.806 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = a \,x^{3}+y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.788 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = a -x^{2} y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.709 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = \left (-x^{2}+1\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = \left (x^{2}-x +1\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.71 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = a \,x^{3}+\left (-2 x^{2}+1\right ) y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.964 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime } = x^{3} \left (-x^{2}+1\right )+\left (-2 x^{2}+1\right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.645 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = 2-4 x^{2} y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.67 |
|
|
\[ {}x \left (x^{2}+1\right ) y^{\prime } = x -\left (5 x^{2}+3\right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.613 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime }+x^{2}+\left (-x^{2}+1\right ) y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.477 |
|
|
\[ {}x^{2} \left (1-x \right ) y^{\prime } = \left (2-x \right ) x y-y^{2} \] |
riccati, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.813 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (x^{2}-y^{2}\right ) y \] |
bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.756 |
|
|
\[ {}2 x^{3} y^{\prime } = \left (3 x^{2}+a y^{2}\right ) y \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.921 |
|
|
\[ {}6 x^{3} y^{\prime } = 4 x^{2} y+\left (1-3 x \right ) y^{4} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.968 |
|
|
\[ {}x \left (c \,x^{2}+b x +a \right ) y^{\prime }+x^{2}-\left (c \,x^{2}+b x +a \right ) y = y^{2} \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.576 |
|
|
\[ {}x^{4} y^{\prime } = \left (x^{3}+y\right ) y \] |
riccati, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.574 |
|
|
\[ {}x^{4} y^{\prime }+a^{2}+x^{4} y^{2} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.111 |
|
|
\[ {}x^{4} y^{\prime }+x^{3} y+\csc \left (x y\right ) = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
5.848 |
|
|
\[ {}\left (-x^{4}+1\right ) y^{\prime } = 2 x \left (1-y^{2}\right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.381 |
|
|
\[ {}x \left (-x^{3}+1\right ) y^{\prime } = 2 x -\left (-4 x^{3}+1\right ) y \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.726 |
|
|
\[ {}x \left (-x^{3}+1\right ) y^{\prime } = x^{2}+\left (1-2 x y\right ) y \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.112 |
|
|
\[ {}x^{2} \left (-x^{2}+1\right ) y^{\prime } = \left (x -3 x^{3} y\right ) y \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}x \left (-2 x^{3}+1\right ) y^{\prime } = 2 \left (-x^{3}+1\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.826 |
|
|
\[ {}\left (c \,x^{2}+b x +a \right )^{2} \left (y^{\prime }+y^{2}\right )+A = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, _Riccati] |
✓ |
✓ |
3.77 |
|
|
\[ {}x^{5} y^{\prime } = 1-3 y x^{4} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.605 |
|
|
\[ {}x \left (-x^{4}+1\right ) y^{\prime } = 2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.354 |
|
|
\[ {}x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3} = 0 \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
61.092 |
|
|
\[ {}x^{n} y^{\prime } = a +b \,x^{n -1} y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.692 |
|
|
\[ {}x^{n} y^{\prime } = x^{2 n -1}-y^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.288 |
|
|
\[ {}x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (-n +1\right ) x^{n -1} = 0 \] |
riccati |
[_Riccati] |
✓ |
✓ |
12.794 |
|
|
\[ {}x^{n} y^{\prime } = a^{2} x^{2 n -2}+y^{2} b^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
3.025 |
|
|
\[ {}x^{n} y^{\prime } = x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.429 |
|
|
\[ {}x^{k} y^{\prime } = a \,x^{m}+b y^{n} \] |
unknown |
[_Chini] |
❇ |
N/A |
0.528 |
|
|
\[ {}y^{\prime } \sqrt {x^{2}+1} = 2 x -y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.746 |
|
|
\[ {}y^{\prime } \sqrt {-x^{2}+1} = 1+y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.656 |
|
|
\[ {}\left (x -\sqrt {x^{2}+1}\right ) y^{\prime } = y+\sqrt {1+y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.009 |
|
|
\[ {}y^{\prime } \sqrt {a^{2}+x^{2}}+x +y = \sqrt {a^{2}+x^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}+x^{2}} = \sqrt {y^{2}+a^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
11.581 |
|
|
\[ {}y^{\prime } \sqrt {b^{2}-x^{2}} = \sqrt {a^{2}-y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}x y^{\prime } \sqrt {a^{2}+x^{2}} = y \sqrt {b^{2}+y^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
9.665 |
|
|
\[ {}x y^{\prime } \sqrt {-a^{2}+x^{2}} = y \sqrt {y^{2}-b^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.847 |
|
|
\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.12 |
|
|
\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.105 |
|
|
\[ {}x^{\frac {3}{2}} y^{\prime } = a +b \,x^{\frac {3}{2}} y^{2} \] |
riccati |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
1.547 |
|
|
\[ {}y^{\prime } \sqrt {x^{3}+1} = \sqrt {y^{3}+1} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
77.213 |
|
|
\[ {}y^{\prime } \sqrt {x \left (1-x \right ) \left (-x a +1\right )} = \sqrt {y \left (1-y\right ) \left (1-a y\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
9.26 |
|
|
\[ {}y^{\prime } \sqrt {-x^{4}+1} = \sqrt {1-y^{4}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.47 |
|
|
\[ {}y^{\prime } \sqrt {x^{4}+x^{2}+1} = \sqrt {1+y^{2}+y^{4}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.326 |
|
|
\[ {}y^{\prime } \sqrt {X} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.059 |
|
|
\[ {}y^{\prime } \sqrt {X}+\sqrt {Y} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.099 |
|
|
\[ {}y^{\prime } \sqrt {X} = \sqrt {Y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.085 |
|
|
\[ {}y^{\prime } \left (x^{3}+1\right )^{\frac {2}{3}}+\left (y^{3}+1\right )^{\frac {2}{3}} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.859 |
|
|
\[ {}y^{\prime } \left (4 x^{3}+\operatorname {a1} x +\operatorname {a0} \right )^{\frac {2}{3}}+\left (\operatorname {a0} +\operatorname {a1} y+4 y^{3}\right )^{\frac {2}{3}} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.793 |
|
|
\[ {}X^{\frac {2}{3}} y^{\prime } = Y^{\frac {2}{3}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.128 |
|
|
\[ {}y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right ) = y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
10.263 |
|
|
\[ {}\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime } = \tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.974 |
|
|
\[ {}\left (1-\sin \left (x \right )\right ) y^{\prime }+y \cos \left (x \right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.358 |
|
|
\[ {}\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y \left (\cos \left (x \right )+\sin \left (x \right )\right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.652 |
|
|
\[ {}\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )+\operatorname {a1} y \sin \left (2 x \right ) = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.44 |
|
|
\[ {}\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (-{\mathrm e}^{x}+1\right ) y = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.624 |
|
|
\[ {}y^{\prime } x \ln \left (x \right ) = a x \left (1+\ln \left (x \right )\right )-y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.815 |
|
|
\[ {}y y^{\prime }+x = 0 \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.987 |
|
|
\[ {}y y^{\prime }+x \,{\mathrm e}^{x^{2}} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.475 |
|
|
\[ {}y y^{\prime }+x^{3}+y = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
0.399 |
|
|
\[ {}y y^{\prime }+x a +b y = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.408 |
|
|
\[ {}y y^{\prime }+x \,{\mathrm e}^{-x} \left (y+1\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.954 |
|
|
\[ {}y y^{\prime }+f \left (x \right ) = g \left (x \right ) y \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
0.362 |
|
|
\[ {}y y^{\prime }+4 \left (1+x \right ) x +y^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.223 |
|
|
\[ {}y y^{\prime } = x a +b y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.854 |
|
|
\[ {}y y^{\prime } = b \cos \left (x +c \right )+a y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.502 |
|
|
\[ {}y y^{\prime } = \operatorname {a0} +\operatorname {a1} y+\operatorname {a2} y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.535 |
|
|
\[ {}y y^{\prime } = x a +b x y^{2} \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.19 |
|
|
\[ {}y y^{\prime } = \csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
21.66 |
|
|
\[ {}y y^{\prime } = \sqrt {y^{2}+a^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.248 |
|
|
\[ {}y y^{\prime } = \sqrt {y^{2}-a^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.211 |
|
|
\[ {}y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right ) = 0 \] |
unknown |
[NONE] |
✗ |
N/A |
1.201 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = x +y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.916 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = x^{2} \left (1-y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.658 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+y = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.407 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.863 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+x -y = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.908 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = x -y \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.351 |
|
|
\[ {}1-y^{\prime } = x +y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.459 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = y \left (2 x y+1\right ) \] |
homogeneousTypeD2, exactWithIntegrationFactor |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.059 |
|
|
\[ {}\left (x +y\right ) y^{\prime }+\tan \left (y\right ) = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.849 |
|
|
\[ {}\left (x -y\right ) y^{\prime } = \left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.217 |
|
|
\[ {}\left (1+x +y\right ) y^{\prime }+1+4 x +3 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.18 |
|
|
\[ {}\left (x +y+2\right ) y^{\prime } = 1-x -y \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}\left (3-x -y\right ) y^{\prime } = 1+x -3 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.21 |
|
|
\[ {}\left (3-x +y\right ) y^{\prime } = 11-4 x +3 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.207 |
|
|
\[ {}\left (y+2 x \right ) y^{\prime }+x -2 y = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.872 |
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|
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