These are ode’s of the form \(y'(x)=f(a+b x+ c y)^{\frac {1}{n}}\) for integer \(n\) and \(n \neq 1\). Also applies to \(y'(x)=f(a+b x+ c y)^m\) for integer \(m\) and \(m \neq 1\). Number of problems in this table is 26
Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = \sqrt {1+x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.654 |
|
|
\[ {}y^{\prime } = \left (4 x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.915 |
|
|
\[ {}y^{\prime } = \sqrt {x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.708 |
|
|
\[ {}y^{\prime } = \frac {1}{x +2 y+1} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.549 |
|
|
\[ {}y^{\prime } = \left (9 x -y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = \left (4 x +y+2\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.72 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.807 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime } = \left (3+x -4 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.947 |
|
|
\[ {}y^{\prime } = \left (1+4 x +9 y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.922 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.852 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime } = \left (1+x +y\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.776 |
|
|
\[ {}y^{\prime } = \sqrt {1+6 x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.671 |
|
|
\[ {}y^{\prime } = \left (1+6 x +y\right )^{\frac {1}{3}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
2.396 |
|
|
\[ {}y^{\prime } = \left (1+6 x +y\right )^{\frac {1}{4}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.289 |
|
|
\[ {}y^{\prime } = \left (a +b x +y\right )^{4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
14.207 |
|
|
\[ {}y^{\prime } = \left (\pi +x +7 y\right )^{\frac {7}{2}} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
7.107 |
|
|
\[ {}y^{\prime } = \left (a +b x +c y\right )^{6} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
4.806 |
|
|
\[ {}y^{\prime } = \left (x +y\right )^{4} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.04 |
|
|
\[ {}y^{\prime }-\left (x +y\right )^{2} = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.865 |
|
|
\[ {}\left (x +y\right ) y^{\prime }-1 = 0 \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.92 |
|
|
\[ {}x^{\prime } = \left (4 t -x\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
2.657 |
|
|
\[ {}x^{\prime } = \left (t +x\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
0.888 |
|
|
\[ {}y^{\prime } = \sqrt {x +y} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.669 |
|
|
\[ {}y^{\prime } = \left (x +y-4\right )^{2} \] |
1 |
1 |
1 |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.074 |
|
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