Number of problems in this table is 38
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) |
|
\[ {}t \left (t -2\right )^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.993 |
|
|
\[ {}\left (-t^{2}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{\sin \left (t +1\right )}+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
28.076 |
|
|
\[ {}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.046 |
|
|
\[ {}x^{3} \left (x^{2}+3\right ) y^{\prime \prime }+5 x y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.705 |
|
|
\[ {}y^{\prime \prime }+\frac {y}{z^{3}} = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.141 |
|
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{x \left (x -3\right )}-\frac {y}{x^{3} \left (x +3\right )} = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.008 |
|
|
\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.415 |
|
|
\[ {}x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.423 |
|
|
\[ {}y^{\prime \prime }+\frac {a y}{x^{\frac {3}{2}}} = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.148 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = x^{\frac {3}{2}} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.134 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.521 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.53 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.331 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.209 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = \frac {1}{x^{4}} \] |
1 |
0 |
0 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.241 |
|
|
\[ {}x^{2} y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.482 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (1+x \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.372 |
|
|
\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.263 |
|
|
\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
4.455 |
|
|
\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.286 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.202 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.342 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 y^{\prime }+3 x^{2} y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.068 |
|
|
\[ {}x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 x y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
6.504 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _missing_y]] |
✗ |
N/A |
0.425 |
|
|
\[ {}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.889 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✗ |
N/A |
0.641 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.927 |
|
|
\[ {}y^{\prime \prime }+5 x y^{\prime }+\sqrt {x}\, y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
8.385 |
|
|
\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.574 |
|
|
\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
6.977 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.56 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.941 |
|
|
\[ {}\left (x^{4}-2 x^{3}+x^{2}\right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }+x^{2} y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.492 |
|
|
\[ {}\left (x^{5}+x^{4}-6 x^{3}\right ) y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.367 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
0 |
0 |
[[_Emden, _Fowler]] |
✗ |
N/A |
0.255 |
|
|
\[ {}x^{2} y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.3 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0 \] |
1 |
0 |
0 |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
5.925 |
|
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