|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}2 \left (1+x \right ) y^{\prime }+2 y+\left (1+x \right )^{4} y^{3} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
0.63 |
|
|
\[ {}3 x y^{\prime } = 3 x^{\frac {2}{3}}+\left (-3 y+1\right ) y \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.006 |
|
|
\[ {}3 x y^{\prime } = \left (2+x y^{3}\right ) y \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.784 |
|
|
\[ {}3 x y^{\prime } = \left (1+3 x y^{3} \ln \left (x \right )\right ) y \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.441 |
|
|
\[ {}x^{2} y^{\prime } = -y+a \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.778 |
|
|
\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}+x y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.619 |
|
|
\[ {}x^{2} y^{\prime } = a +b x +c \,x^{2}-x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}x^{2} y^{\prime }+\left (1-2 x \right ) y = x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.543 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.555 |
|
|
\[ {}x^{2} y^{\prime } = \left (b x +a \right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.684 |
|
|
\[ {}x^{2} y^{\prime }+x \left (2+x \right ) y = x \left (1-{\mathrm e}^{-2 x}\right )-2 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.626 |
|
|
\[ {}x^{2} y^{\prime }+2 x \left (1-x \right ) y = {\mathrm e}^{x} \left (2 \,{\mathrm e}^{x}-1\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}x^{2} y^{\prime }+x^{2}+x y+y^{2} = 0 \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.688 |
|
|
\[ {}x^{2} y^{\prime } = \left (1+2 x -y\right )^{2} \] |
riccati, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.639 |
|
|
\[ {}x^{2} y^{\prime } = a +b y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.772 |
|
|
\[ {}x^{2} y^{\prime } = \left (a y+x \right ) y \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}x^{2} y^{\prime } = \left (x a +b y\right ) y \] |
riccati, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.786 |
|
|
\[ {}x^{2} y^{\prime }+x^{2} a +b x y+c y^{2} = 0 \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.764 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{n}+x^{2} y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.918 |
|
|
\[ {}x^{2} y^{\prime }+2+x y \left (4+x y\right ) = 0 \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.003 |
|
|
\[ {}x^{2} y^{\prime }+2+a x \left (1-x y\right )-x^{2} y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.275 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{2} y^{2} \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
1.735 |
|
|
\[ {}x^{2} y^{\prime } = a +b \,x^{n}+c \,x^{2} y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.972 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{2} y^{2} \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
2.024 |
|
|
\[ {}x^{2} y^{\prime } = a +b x y+c \,x^{4} y^{2} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.576 |
|
|
\[ {}x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y = 0 \] |
bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.843 |
|
|
\[ {}x^{2} y^{\prime } = 2 y \left (x -y^{2}\right ) \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.528 |
|
|
\[ {}x^{2} y^{\prime } = a \,x^{2} y^{2}-a y^{3} \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
1.148 |
|
|
\[ {}x^{2} y^{\prime }+a y^{2}+b \,x^{2} y^{3} = 0 \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
1.58 |
|
|
\[ {}x^{2} y^{\prime } = \left (x a +b y^{3}\right ) y \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.39 |
|
|
\[ {}x^{2} y^{\prime }+x y+\sqrt {y} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.869 |
|
|
\[ {}x^{2} y^{\prime } = \sec \left (y\right )+3 x \tan \left (y\right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.119 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = -x^{2}+y+1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.68 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+1 = x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.638 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 5-x y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.663 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+a +x y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.552 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+a -x y = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.687 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+a -x y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.573 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x +x y = 0 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.63 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }-x^{2}+x y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.615 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+x^{2}+x y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.617 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (x^{2}+1\right ) x -x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.511 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \left (3 x^{2}-y\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.514 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.552 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x -y\right ) \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.527 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 2 x \left (x^{2}+1\right )^{2}+2 x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.504 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime }+\cos \left (x \right ) = 2 x y \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.158 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \tan \left (x \right )-2 x y \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.573 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = a +4 x y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.566 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \left (2 b x +a \right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.69 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.555 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.515 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = 1-\left (2 x -y\right ) y \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.006 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = n \left (1-2 x y+y^{2}\right ) \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.596 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right ) = 0 \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.104 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y \left (1+a y\right ) \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.698 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+y^{2}-2 x y \left (1+y^{2}\right ) \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
65.437 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right ) = x \left (x^{2}+1\right ) \cos \left (y\right )^{2} \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.553 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = 1+x^{2}-y \,\operatorname {arccot}\left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.236 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime }+4 y = \left (2+x \right ) y^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.651 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = b +x y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.928 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = \left (b +y\right ) \left (x +\sqrt {a^{2}+x^{2}}\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.938 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+\left (x -y\right ) y = 0 \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.622 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime } = a^{2}+3 x y-2 y^{2} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, _Riccati] |
✓ |
✓ |
3.102 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime }+x y+b x y^{2} = 0 \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.346 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = a +\left (1+x \right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.7 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = 2 x y+2 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.61 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = 2 x y-2 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.554 |
|
|
\[ {}x \left (1+x \right ) y^{\prime } = \left (1-2 x \right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.655 |
|
|
\[ {}x \left (1-x \right ) y^{\prime }+\left (2 x +1\right ) y = a \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.641 |
|
|
\[ {}x \left (1-x \right ) y^{\prime } = a +2 \left (2-x \right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.671 |
|
|
\[ {}x \left (1-x \right ) y^{\prime }+2-3 x y+y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.667 |
|
|
\[ {}x \left (1+x \right ) y^{\prime } = \left (1+x \right ) \left (x^{2}-1\right )+\left (x^{2}+x -1\right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.694 |
|
|
\[ {}\left (-2+x \right ) \left (x -3\right ) y^{\prime }+x^{2}-8 y+3 x y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.669 |
|
|
\[ {}x \left (x +a \right ) y^{\prime } = \left (b +c y\right ) y \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.375 |
|
|
\[ {}\left (x +a \right )^{2} y^{\prime } = 2 \left (x +a \right ) \left (b +y\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.874 |
|
|
\[ {}\left (x -a \right )^{2} y^{\prime }+k \left (x +y-a \right )^{2}+y^{2} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, _Riccati] |
✓ |
✓ |
1.631 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.49 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime } = \left (x -a \right ) \left (-b +x \right )+\left (2 x -a -b \right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.894 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime } = c y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.829 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (y-a \right ) \left (y-b \right ) = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.154 |
|
|
\[ {}\left (x -a \right ) \left (-b +x \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2} = 0 \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
2.243 |
|
|
\[ {}2 x^{2} y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.647 |
|
|
\[ {}2 x^{2} y^{\prime }+x \cot \left (x \right )-1+2 x^{2} y \cot \left (x \right ) = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.017 |
|
|
\[ {}2 x^{2} y^{\prime }+1+2 x y-x^{2} y^{2} = 0 \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
0.979 |
|
|
\[ {}2 x^{2} y^{\prime } = 2 x y+\left (1-x \cot \left (x \right )\right ) \left (x^{2}-y^{2}\right ) \] |
riccati, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
1.714 |
|
|
\[ {}2 \left (-x^{2}+1\right ) y^{\prime } = \sqrt {-x^{2}+1}+\left (1+x \right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.693 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime }+1+\left (1-4 x \right ) y = 0 \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.632 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime } = 4 x -\left (1+4 x \right ) y+y^{2} \] |
riccati, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
1.909 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime }+x +\left (1-2 x \right ) y = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.797 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime }+x +\left (1-x \right ) y^{2} = 0 \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.364 |
|
|
\[ {}2 \left (x^{2}+x +1\right ) y^{\prime } = 1+8 x^{2}-\left (2 x +1\right ) y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.979 |
|
|
\[ {}4 \left (x^{2}+1\right ) y^{\prime }-4 x y-x^{2} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.651 |
|
|
\[ {}a \,x^{2} y^{\prime } = x^{2}+a x y+y^{2} b^{2} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
0.956 |
|
|
\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = A +B y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.681 |
|
|
\[ {}\left (b \,x^{2}+a \right ) y^{\prime } = c x y \ln \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.227 |
|
|
\[ {}x \left (x a +1\right ) y^{\prime }+a -y = 0 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.753 |
|
|
\[ {}\left (b x +a \right )^{2} y^{\prime }+c y^{2}+\left (b x +a \right ) y^{3} = 0 \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
4.153 |
|
|
\[ {}x^{3} y^{\prime } = a +b \,x^{2} y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.656 |
|
|
\[ {}x^{3} y^{\prime } = 3-x^{2}+x^{2} y \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.605 |
|
|
|
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|
|
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