|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{2} y^{\prime \prime }+6 y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.183 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}+5 y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
5.925 |
|
|
\[ {}\left (x^{2}-3 x -4\right ) y^{\prime \prime }-\left (1+x \right ) y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.627 |
|
|
\[ {}\left (x^{2}-25\right )^{2} y^{\prime \prime }-\left (x +5\right ) y^{\prime }+10 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.745 |
|
|
\[ {}2 x y^{\prime \prime }-5 y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.558 |
|
|
\[ {}5 x y^{\prime \prime }+8 y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.401 |
|
|
\[ {}9 x y^{\prime \prime }+14 y^{\prime }+\left (-1+x \right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.966 |
|
|
\[ {}7 x y^{\prime \prime }+10 y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.066 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-1+x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.704 |
|
|
\[ {}x y^{\prime \prime }+2 x y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.007 |
|
|
\[ {}y^{\prime \prime }+\frac {8 y^{\prime }}{3 x}-\left (\frac {2}{3 x^{2}}-1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.533 |
|
|
\[ {}y^{\prime \prime }+\left (\frac {16}{3 x}-1\right ) y^{\prime }-\frac {16 y}{3 x^{2}} = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.69 |
|
|
\[ {}y^{\prime \prime }+\left (\frac {1}{2 x}-2\right ) y^{\prime }-\frac {35 y}{16 x^{2}} = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.348 |
|
|
\[ {}y^{\prime \prime }-\left (\frac {1}{x}+2\right ) y^{\prime }+\left (x +\frac {1}{x^{2}}\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.827 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }-7 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.222 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.137 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.024 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.681 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-k^{2}+x^{2}\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Bessel] |
✓ |
✓ |
2.056 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+k \left (k +1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.566 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {1}{2}-3 x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.63 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.405 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Jacobi] |
✓ |
✓ |
1.47 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+k y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Laguerre] |
✓ |
✓ |
1.949 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.449 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (16 x^{2}-25\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.785 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.341 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.333 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.562 |
|
|
\[ {}\left (t +1\right )^{2} y^{\prime \prime }-2 \left (t +1\right ) y^{\prime }+2 y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.749 |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+t y = 0 \] |
reduction_of_order |
[_Lienard] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.357 |
|
|
\[ {}6 y^{\prime \prime }+5 y^{\prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.414 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.345 |
|
|
\[ {}y^{\prime \prime }-10 y^{\prime }+34 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.772 |
|
|
\[ {}2 y^{\prime \prime }-5 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.362 |
|
|
\[ {}15 y^{\prime \prime }-11 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.365 |
|
|
\[ {}20 y^{\prime \prime }+y^{\prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.366 |
|
|
\[ {}12 y^{\prime \prime }+8 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.359 |
|
|
\[ {}2 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.329 |
|
|
\[ {}9 y^{\prime \prime \prime }+36 y^{\prime \prime }+40 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.503 |
|
|
\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+13 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.5 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = -t \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.536 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 5 t^{2} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.464 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = -3 \sin \left (t \right ) \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.441 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 3 \sin \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.237 |
|
|
\[ {}y^{\prime \prime }-9 y = \frac {1}{1+{\mathrm e}^{3 t}} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.692 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \frac {1}{{\mathrm e}^{2 t}+1} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.274 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = -4 \,{\mathrm e}^{-2 t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.534 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 3 \,{\mathrm e}^{-2 t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.025 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime }+20 y = -2 \,{\mathrm e}^{t} t \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.578 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 t^{2} {\mathrm e}^{-4 t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.593 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-9 y^{\prime }+5 y = {\mathrm e}^{t} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.766 |
|
|
\[ {}y^{\prime \prime \prime }-12 y^{\prime }-16 y = {\mathrm e}^{4 t}-{\mathrm e}^{-2 t} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.961 |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+18 y^{\prime \prime }+30 y^{\prime }+25 y = {\mathrm e}^{-t} \cos \left (2 t \right )+{\mathrm e}^{-2 t} \sin \left (t \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
53.383 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+14 y^{\prime \prime }+20 y^{\prime }+25 y = t^{2} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
0.361 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.624 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.389 |
|
|
\[ {}y^{\prime \prime }+25 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
4.296 |
|
|
\[ {}y^{\prime \prime }-4 y = t \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.78 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = {\mathrm e}^{t} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.86 |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.433 |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.158 |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.697 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = \frac {{\mathrm e}^{4 t}}{t^{3}} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
❇ |
N/A |
0.809 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{t} \ln \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.311 |
|
|
\[ {}y^{\prime \prime }-2 t y^{\prime }+t^{2} y = 0 \] |
kovacic, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.487 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.351 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.41 |
|
|
\[ {}t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.047 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+8 y = 0 \] |
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]] |
✓ |
✓ |
2.328 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
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_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.554 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
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)]‘]] |
✓ |
✓ |
2.039 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y = 0 \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, 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 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
6.456 |
|
|
\[ {}5 x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
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]] |
✓ |
✓ |
2.429 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+25 y = 0 \] |
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]] |
✓ |
✓ |
2.359 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+15 y = 8 x \] |
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 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.712 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.025 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = x \,{\mathrm e}^{x} \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.16 |
|
|
\[ {}\left (2 x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.023 |
|
|
\[ {}3 x y^{\prime \prime }+11 y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.482 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+5 x y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.13 |
|
|
\[ {}x^{2} y^{\prime \prime }-7 x y^{\prime }+\left (-2 x^{2}+7\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.89 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }+10 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Jacobi] |
✓ |
✓ |
1.582 |
|
|
\[ {}x \left (1+x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }-10 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.648 |
|
|
\[ {}t \left (y y^{\prime \prime }+{y^{\prime }}^{2}\right )+y^{\prime } y = 1 \] |
second_order_integrable_as_is |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.648 |
|
|
\[ {}4 x^{\prime \prime }+9 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.311 |
|
|
\[ {}9 x^{\prime \prime }+4 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
7.336 |
|
|
\[ {}x^{\prime \prime }+64 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
16.018 |
|
|
\[ {}x^{\prime \prime }+100 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
11.646 |
|
|
\[ {}x^{\prime \prime }+x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.997 |
|
|
\[ {}x^{\prime \prime }+4 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.296 |
|
|
\[ {}x^{\prime \prime }+16 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.678 |
|
|
\[ {}x^{\prime \prime }+256 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
27.919 |
|
|
\[ {}x^{\prime \prime }+9 x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.13 |
|
|
|
||||||
|
|
||||||