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) |
|
\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.944 |
|
|
\[ {}\left (x^{2}-25\right ) y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.046 |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.242 |
|
|
\[ {}\left (x^{2}-2 x +10\right ) y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime \prime }-x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.388 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.417 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Lienard] |
✓ |
✓ |
0.623 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Hermite] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.594 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.529 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.513 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.757 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.653 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-6 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.441 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.774 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.58 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.497 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2-x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.58 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+8 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.85 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime \prime }+y \sin \left (x \right ) = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.974 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{x} y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.783 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.514 |
|
|
\[ {}x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }+3 y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.263 |
|
|
\[ {}x \left (x +3\right )^{2} y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.356 |
|
|
\[ {}\left (x^{2}-9\right )^{2} y^{\prime \prime }+\left (x +3\right ) y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.428 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{x}+\frac {y}{\left (-1+x \right )^{3}} = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.741 |
|
|
\[ {}\left (x^{3}+4 x \right ) y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.747 |
|
|
\[ {}x^{2} \left (x -5\right )^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.619 |
|
|
\[ {}\left (x^{2}+x -6\right ) y^{\prime \prime }+\left (x +3\right ) y^{\prime }+\left (-2+x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.285 |
|
|
\[ {}x \left (x^{2}+1\right )^{2} y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.371 |
|
|
\[ {}x^{3} \left (x^{2}-25\right ) \left (-2+x \right )^{2} y^{\prime \prime }+3 x \left (-2+x \right ) y^{\prime }+7 \left (x +5\right ) y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
4.455 |
|
|
\[ {}\left (x^{3}-2 x^{2}+3 x \right )^{2} y^{\prime \prime }+x \left (x -3\right )^{2} y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.415 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+5 \left (1+x \right ) y^{\prime }+\left (x^{2}-x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.198 |
|
|
\[ {}x y^{\prime \prime }+\left (x +3\right ) y^{\prime }+7 x^{2} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.582 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (\frac {5}{3} x +x^{2}\right ) y^{\prime }-\frac {y}{3} = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.121 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.833 |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.905 |
|
|
\[ {}2 x y^{\prime \prime }+5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.89 |
|
|
\[ {}4 x y^{\prime \prime }+\frac {y^{\prime }}{2}+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.889 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.924 |
|
|
\[ {}3 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.061 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {2}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.835 |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x +3\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[_Laguerre] |
✓ |
✓ |
1.131 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {4}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.899 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x^{2} y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.939 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (2 x -1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.298 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.832 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.994 |
|
|
\[ {}x y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.98 |
|
|
\[ {}y^{\prime \prime }+\frac {3 y^{\prime }}{x}-2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.066 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.846 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.875 |
|
|
\[ {}x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.284 |
|
|
\[ {}x \left (-1+x \right ) y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.985 |
|
|
\[ {}x^{4} y^{\prime \prime }+\lambda y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.286 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.202 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _exact, _linear, _homogeneous]] |
❇ |
N/A |
0.342 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.908 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
2.938 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-25\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.084 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+16 x y^{\prime }+\left (16 x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.933 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
0.702 |
|
|
\[ {}y^{\prime }+x y^{\prime \prime }+\left (x -\frac {4}{x}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
2.836 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (9 x^{2}-4\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.777 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (36 x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.009 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (25 x^{2}-\frac {4}{9}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.812 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (2 x^{2}-64\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.53 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.089 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.964 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.952 |
|
|
\[ {}x y^{\prime \prime }-5 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.888 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.863 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (16 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.827 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+x^{3} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.922 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+9 x y^{\prime }+\left (x^{6}-36\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.916 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.407 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-7 x^{3} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.873 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.378 |
|
|
\[ {}x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.931 |
|
|
\[ {}16 x^{2} y^{\prime \prime }+32 x y^{\prime }+\left (x^{4}-12\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (16 x^{4}+3\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.965 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.892 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.541 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.632 |
|
|
\[ {}y^{\prime \prime }-x^{2} y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.708 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
0.957 |
|
|
\[ {}\cos \left (x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.364 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.58 |
|
|
\[ {}\left (2+x \right ) y^{\prime \prime }+3 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.421 |
|
|
|
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