Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}5 x y+4 y^{2}+1+\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.361 |
|
|
\[ {}2 x \tan \left (y\right )+\left (x -x^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
1.694 |
|
|
\[ {}y^{2} \left (x^{2}+1\right )+y+\left (2 x y+1\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.912 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.534 |
|
|
\[ {}5 x +2 y+1+\left (2 x +y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.762 |
|
|
\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.983 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.013 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.622 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.014 |
|
|
\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.457 |
|
|
|
|||||||||
|
|
|||||||||