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) |
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.432 |
|
|
\[ {}y^{\prime \prime }+4 x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.502 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.546 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.402 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.447 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.502 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.648 |
|
|
\[ {}y^{\prime \prime }+2 x^{3} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime \prime }-x y = \frac {1}{1-x} \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.446 |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.704 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.003 |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.657 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}-x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.829 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }-x^{2} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.877 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.772 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.357 |
|
|
\[ {}x^{2} y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.482 |
|
|
\[ {}x y^{\prime \prime }+x^{3} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.458 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.292 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.484 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.389 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (1+x \right ) y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.372 |
|
|
\[ {}x y^{\prime \prime }+x^{5} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.616 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.315 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }-y \sin \left (x \right ) = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.514 |
|
|
\[ {}x^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.619 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x -\frac {3}{4}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.823 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.803 |
|
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