|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.352 |
|
|
\[ {}\left (-4 x^{2}+1\right ) y^{\prime \prime }+6 x y^{\prime }-4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
2.733 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+3 x y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.287 |
|
|
\[ {}y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+5 x y^{\prime }+3 y = 0 \] |
unknown |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✗ |
N/A |
0.094 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+3 y = x^{2} \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.465 |
|
|
\[ {}y^{\prime \prime }+3 x y^{\prime }+7 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.521 |
|
|
\[ {}2 y^{\prime \prime }+9 x y^{\prime }-36 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.346 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
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)]‘]] |
✓ |
✓ |
0.402 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }+3 x y^{\prime }-8 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.399 |
|
|
\[ {}\left (9 x^{2}+1\right ) y^{\prime \prime }-18 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.351 |
|
|
\[ {}\left (3 x^{2}+1\right ) y^{\prime \prime }+13 x y^{\prime }+7 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.476 |
|
|
\[ {}\left (2 x^{2}+1\right ) y^{\prime \prime }+11 x y^{\prime }+9 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime \prime }+\left (-2+x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.365 |
|
|
\[ {}\left (x^{2}-2 x +2\right ) y^{\prime \prime }-4 \left (-1+x \right ) y^{\prime }+6 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.389 |
|
|
\[ {}2 x \left (1+x \right ) y^{\prime \prime }+3 \left (1+x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.081 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}-1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.935 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x y^{\prime }-\left (4 x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.307 |
|
|
\[ {}4 x y^{\prime \prime }+3 y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.696 |
|
|
\[ {}2 x^{2} \left (1-x \right ) y^{\prime \prime }-x \left (1+7 x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.773 |
|
|
\[ {}2 x y^{\prime \prime }+5 \left (1-2 x \right ) y^{\prime }-5 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.206 |
|
|
\[ {}8 x^{2} y^{\prime \prime }+10 x y^{\prime }-y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.876 |
|
|
\[ {}2 x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.6 |
|
|
\[ {}2 x \left (x +3\right ) y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.988 |
|
|
\[ {}2 x y^{\prime \prime }+\left (-2 x^{2}+1\right ) y^{\prime }-4 x y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.647 |
|
|
\[ {}x \left (4-x \right ) y^{\prime \prime }+\left (2-x \right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.082 |
|
|
\[ {}3 x^{2} y^{\prime \prime }+x y^{\prime }-y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.714 |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.099 |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-5 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.172 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x \left (1-x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.211 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x \left (4 x -1\right ) y^{\prime }+2 \left (3 x -1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.094 |
|
|
\[ {}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.619 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.11 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.115 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.049 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.116 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.52 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.355 |
|
|
\[ {}9 x^{2} y^{\prime \prime }+2 y = 0 \] |
kovacic, second_order_euler_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.414 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.201 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.175 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.277 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.403 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.388 |
|
|
\[ {}x^{2} y^{\prime \prime }+5 x y^{\prime }+5 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.615 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 x y^{\prime }+8 y = 0 \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.546 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.404 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.422 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.481 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.345 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.598 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.675 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (-1+x \right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.529 |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.563 |
|
|
\[ {}x \left (-2+x \right ) y^{\prime \prime }+2 \left (-1+x \right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.665 |
|
|
\[ {}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.117 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-x y = 0 \] |
second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.581 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.156 |
|
|
\[ {}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.358 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.818 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x \left (1+x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.729 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x \left (1+x \right ) y^{\prime }+\left (1-3 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.703 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.408 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x \left (-2+x \right ) y^{\prime }+2 \left (2-3 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.983 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (6 x +1\right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.066 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (3 x +2\right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
1.937 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.132 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (x +5\right ) y^{\prime }-4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.178 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.834 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.644 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.109 |
|
|
\[ {}x y^{\prime \prime }+\left (3 x +4\right ) y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.885 |
|
|
\[ {}x y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.036 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.912 |
|
|
\[ {}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.949 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+8 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.108 |
|
|
\[ {}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.567 |
|
|
\[ {}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.217 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.102 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (3+4 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.342 |
|
|
\[ {}2 x y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.357 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.632 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.472 |
|
|
\[ {}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.535 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Jacobi] |
✓ |
✓ |
2.27 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Jacobi] |
✓ |
✓ |
2.376 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
second_order_bessel_ode |
[_Bessel] |
✓ |
✓ |
0.661 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
2.136 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (8+5 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.368 |
|
|
\[ {}x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-5 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
2.562 |
|
|
\[ {}9 x^{2} y^{\prime \prime }-15 x y^{\prime }+7 y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.523 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.598 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+\left (x^{3}+x +1\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.152 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
2.543 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+x \left (1+x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.639 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.129 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }+\left (x^{4}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.507 |
|
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.171 |
|
|
|
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