|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime }+y = \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.008 |
|
|
\[ {}y^{\prime \prime } = -3 y \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
13.961 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.572 |
|
|
\[ {}y^{\prime } = 2 x y \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.259 |
|
|
\[ {}y^{\prime } = 2 x y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}y^{\prime }+y = 1 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.225 |
|
|
\[ {}y^{\prime }+y = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.392 |
|
|
\[ {}y^{\prime }-y = 2 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.184 |
|
|
\[ {}y^{\prime }-y = 2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime }+y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime }+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.235 |
|
|
\[ {}y^{\prime }-y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.718 |
|
|
\[ {}y^{\prime }-y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.205 |
|
|
\[ {}y^{\prime }-y = x^{2} \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime }-y = x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.397 |
|
|
\[ {}x y^{\prime } = y \] |
first order ode series method. Regular singular point |
[_separable] |
✓ |
✓ |
0.7 |
|
|
\[ {}x y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.5 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
first order ode series method. Irregular singular point |
[_separable] |
❇ |
N/A |
0.833 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.664 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
first order ode series method. Regular singular point |
[_linear] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.743 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.173 |
|
|
\[ {}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}} \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.063 |
|
|
\[ {}y^{\prime } = y+1 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.765 |
|
|
\[ {}y^{\prime } = x -y \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[[_linear, ‘class A‘]] |
✓ |
✓ |
7.867 |
|
|
\[ {}y^{\prime } = x -y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-y = x \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.941 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x^{2} y = 1 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.894 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.433 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.254 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.583 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.191 |
|
|
\[ {}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.589 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.573 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 p y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.516 |
|
|
\[ {}x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 x y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
6.504 |
|
|
\[ {}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
10.205 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _missing_y]] |
❇ |
N/A |
0.425 |
|
|
\[ {}\left (1+3 x \right ) x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.423 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.463 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.506 |
|
|
\[ {}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.851 |
|
|
\[ {}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.432 |
|
|
\[ {}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
2.889 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
39.095 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.792 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
7.579 |
|
|
\[ {}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.538 |
|
|
\[ {}4 x y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.832 |
|
|
\[ {}2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.984 |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.271 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.92 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
2.013 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
❇ |
N/A |
0.641 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _exact, _linear, _homogeneous]] |
❇ |
N/A |
0.927 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.501 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.294 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.411 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.453 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.519 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-3 \left (-1+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.141 |
|
|
\[ {}3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.967 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
6.876 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.597 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
3.153 |
|
|
\[ {}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.782 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.117 |
|
|
\[ {}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
24.812 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
4.711 |
|
|
\[ {}\left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+{\mathrm e}^{x} y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.176 |
|
|
\[ {}y^{\prime \prime }+2 x y = x^{2} \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.428 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = x \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.408 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}-x \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.9 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.777 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.219 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.997 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.751 |
|
|
\[ {}\left (x^{2}+1\right ) x^{2} y^{\prime \prime }-x y^{\prime }+\left (2+x \right ) y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.607 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.891 |
|
|
\[ {}x y^{\prime \prime }-4 y^{\prime }+x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
3.286 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.754 |
|
|
\[ {}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.217 |
|
|
\[ {}x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Laguerre] |
✓ |
✓ |
3.061 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.414 |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.652 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (-1+x \right ) y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.698 |
|
|
\[ {}9 \left (-2+x \right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (-2+x \right ) y^{\prime }+16 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
24.606 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Gegenbauer] |
✓ |
✓ |
5.185 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.156 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \] |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.085 |
|
|
|
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