|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+16 y = \delta \left (t -2\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.061 |
|
|
\[ {}y^{\prime \prime }-16 y = \delta \left (t -10\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.053 |
|
|
\[ {}y^{\prime \prime }+y = \delta \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.733 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.936 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-12 y = \delta \left (t -3\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.296 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = \delta \left (t -4\right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.979 |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+45 y = \delta \left (t \right ) \] |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
0.967 |
|
|
\[ {}y^{\prime \prime \prime }+9 y^{\prime } = \delta \left (-1+t \right ) \] |
higher_order_laplace |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.954 |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y = \delta \left (t \right ) \] |
higher_order_laplace |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✗ |
3.119 |
|
|
\[ {}y^{\prime }-2 y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.687 |
|
|
\[ {}y^{\prime }-2 x y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime }+\frac {2 y}{2 x -1} = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.599 |
|
|
\[ {}\left (x -3\right ) y^{\prime }-2 y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.537 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-2 x y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.451 |
|
|
\[ {}y^{\prime }+\frac {y}{-1+x} = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.584 |
|
|
\[ {}y^{\prime }+\frac {y}{-1+x} = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.532 |
|
|
\[ {}\left (1-x \right ) y^{\prime }-2 y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.664 |
|
|
\[ {}\left (-x^{3}+2\right ) y^{\prime }-3 x^{2} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.634 |
|
|
\[ {}\left (-x^{3}+2\right ) y^{\prime }+3 x^{2} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.55 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-x y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.624 |
|
|
\[ {}\left (1+x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.684 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.634 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.757 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.624 |
|
|
\[ {}y^{\prime \prime }-3 x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.682 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }-5 x y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.056 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.883 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+6 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.042 |
|
|
\[ {}\left (x^{2}-6 x \right ) y^{\prime \prime }+4 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.237 |
|
|
\[ {}y^{\prime \prime }+\left (2+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.145 |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.981 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-2 x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.004 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\lambda y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.175 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.141 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.535 |
|
|
\[ {}y^{\prime \prime }-x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.559 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{2 x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.727 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.102 |
|
|
\[ {}y^{\prime \prime }+x y = \sin \left (x \right ) \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.025 |
|
|
\[ {}y^{\prime \prime }-\sin \left (x \right ) y^{\prime }-x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.483 |
|
|
\[ {}y^{\prime \prime }-y^{2} = 0 \] |
second order series method. Taylor series method |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
8.054 |
|
|
\[ {}y^{\prime }+\cos \left (y\right ) = 0 \] |
first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.87 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.733 |
|
|
\[ {}y^{\prime }-\tan \left (x \right ) y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.992 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-{\mathrm e}^{x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
87.506 |
|
|
\[ {}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-{\mathrm e}^{x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.42 |
|
|
\[ {}\sinh \left (x \right ) y^{\prime \prime }+x^{2} y^{\prime }-y \sin \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
172.314 |
|
|
\[ {}{\mathrm e}^{3 x} y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+\frac {2 y}{x^{2}+4} = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
28.862 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (1+{\mathrm e}^{x}\right ) y}{-{\mathrm e}^{x}+1} = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.645 |
|
|
\[ {}\left (x^{2}-4\right ) y^{\prime \prime }+\left (x^{2}+x -6\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.214 |
|
|
\[ {}x y^{\prime \prime }+\left (-{\mathrm e}^{x}+1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.217 |
|
|
\[ {}\sin \left (\pi \,x^{2}\right ) y^{\prime \prime }+x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.764 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.621 |
|
|
\[ {}y^{\prime }+{\mathrm e}^{2 x} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.686 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime }+y \ln \left (x \right ) = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.01 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.3 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }-{\mathrm e}^{x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.239 |
|
|
\[ {}x y^{\prime \prime }-3 x y^{\prime }+y \sin \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.786 |
|
|
\[ {}y^{\prime \prime }+y \ln \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Titchmarsh] |
✓ |
✓ |
1.066 |
|
|
\[ {}\sqrt {x}\, y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.191 |
|
|
\[ {}y^{\prime \prime }+\left (6 x^{2}+2 x +1\right ) y^{\prime }+\left (2+12 x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.326 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.969 |
|
|
\[ {}y^{\prime }+y \sqrt {x^{2}+1} = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.208 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }+y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.845 |
|
|
\[ {}y^{\prime }+\sqrt {2 x^{2}+1}\, y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.302 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{x} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime \prime }+y \cos \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.992 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+y \cos \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.44 |
|
|
\[ {}\sqrt {x}\, y^{\prime \prime }+y^{\prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.071 |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }-2 \left (x -3\right ) y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.005 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.0 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-5 \left (-1+x \right ) y^{\prime }+9 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }+\left (2+x \right ) y^{\prime } = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.795 |
|
|
\[ {}3 \left (-2+x \right )^{2} y^{\prime \prime }-4 \left (x -5\right ) y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.511 |
|
|
\[ {}\left (x -5\right )^{2} y^{\prime \prime }+\left (x -5\right ) y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.296 |
|
|
\[ {}x^{2} y^{\prime \prime }+\frac {x y^{\prime }}{-2+x}+\frac {2 y}{2+x} = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.737 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.245 |
|
|
\[ {}\left (-x^{4}+x^{3}\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+827 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.955 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x -3}+\frac {y}{x -4} = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.136 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{\left (x -3\right )^{2}}+\frac {y}{\left (x -4\right )^{2}} = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.844 |
|
|
\[ {}y^{\prime \prime }+\left (\frac {1}{x}-\frac {1}{3}\right ) y^{\prime }+\left (\frac {1}{x}-\frac {1}{4}\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.148 |
|
|
\[ {}\left (4 x^{2}-1\right ) y^{\prime \prime }+\left (4-\frac {2}{x}\right ) y^{\prime }+\frac {\left (-x^{2}+1\right ) y}{x^{2}+1} = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.801 |
|
|
\[ {}\left (x^{2}+4\right )^{2} y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.651 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (x^{2}+2\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.18 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.11 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-4+4 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.79 |
|
|
\[ {}\left (-9 x^{4}+x^{2}\right ) y^{\prime \prime }-6 x y^{\prime }+10 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.319 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+\frac {y}{1-x} = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.257 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
1.086 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+\left (1-\frac {1}{x^{2}}\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
2.846 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+\left (-2 x^{3}+5 x \right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.73 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+\left (9+4 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.265 |
|
|
\[ {}\left (-3 x^{3}+3 x^{2}\right ) y^{\prime \prime }-\left (5 x^{2}+4 x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.589 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
3.245 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x^{2} y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.282 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (-x^{4}+x \right ) y^{\prime }+3 x^{3} y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.655 |
|
|
\[ {}\left (9 x^{3}+9 x^{2}\right ) y^{\prime \prime }+\left (27 x^{2}+9 x \right ) y^{\prime }+\left (8 x -1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.417 |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.125 |
|
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