|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+a^{2} y = 2 \cos \left (m x \right )+3 \sin \left (m x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.224 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = {\mathrm e}^{x} \sin \left (x \right ) \] |
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]] |
✓ |
✓ |
2.687 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 4 \left (\cos \left (x \right )+\sin \left (x \right )\right ) {\mathrm e}^{x} \] |
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]] |
✓ |
✓ |
4.516 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 10 \,{\mathrm e}^{-2 x} \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.906 |
|
|
\[ {}4 y^{\prime \prime }+8 y^{\prime } = x \sin \left (x \right ) \] |
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]] |
✓ |
✓ |
5.262 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = x \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{2} {\mathrm e}^{4 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \left (x^{2}+x \right ) {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = x^{2}+x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.436 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
1.724 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = x^{3} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime } = x^{2}+x \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.234 |
|
|
\[ {}y^{\prime \prime }+y = x^{2} \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.147 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = x^{2} {\mathrm e}^{-x} \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.021 |
|
|
\[ {}y^{\prime \prime \prime }-y = \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.694 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y = \cos \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.234 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y = {\mathrm e}^{x} \cos \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.241 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = {\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.991 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{x}+{\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.628 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = x +{\mathrm e}^{-4 x} \] |
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]] |
✓ |
✓ |
2.099 |
|
|
\[ {}y^{\prime \prime }-y = x +\sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.757 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = \left (\sin \left (x \right )+1\right ) {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.906 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime } = 1+{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.187 |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime } = {\mathrm e}^{2 x}+\sin \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.992 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.778 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime } = 2 \cos \left (4 x \right )^{2} \] |
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]] |
✓ |
✓ |
5.691 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 4 x -2 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.56 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 18 x -10 \cos \left (x \right ) \] |
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]] |
✓ |
✓ |
4.339 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2+{\mathrm e}^{x} \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.815 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \left (5 x +4\right ) {\mathrm e}^{x}+{\mathrm e}^{-x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.892 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \,{\mathrm e}^{-x}+17 \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.145 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }-2 y = 5 \,{\mathrm e}^{x} \cosh \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime \prime }+4 y = x \sin \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.514 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = x \,{\mathrm e}^{x}+\frac {\cos \left (x \right )}{2} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.379 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \cos \left (x \right )^{2}+{\mathrm e}^{x}+x^{2} \] |
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]] |
✓ |
✓ |
10.406 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime } = {\mathrm e}^{x}+3 \sin \left (2 x \right )+1 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.35 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 10 \sin \left (x \right )+17 \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.356 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = x^{2}-{\mathrm e}^{-x}+{\mathrm e}^{x} \] |
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]] |
✓ |
✓ |
2.491 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 2 x +{\mathrm e}^{-x}-2 \,{\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.839 |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{x}+4 \sin \left (2 x \right )+2 \cos \left (x \right )^{2}-1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.427 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 6 x \,{\mathrm e}^{-x} \left (1-{\mathrm e}^{-x}\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.811 |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (2 x \right )^{2}+\sin \left (\frac {x}{2}\right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.928 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 1+8 \cos \left (x \right )+{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.629 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (\frac {x}{2}\right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right ) \] |
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]] |
✓ |
✓ |
2.404 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = {\mathrm e}^{x} \left (1-2 \sin \left (x \right )^{2}\right )+10 x +1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.007 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 4 x +\sin \left (x \right )+\sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.831 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 1+2 \cos \left (x \right )+\cos \left (2 x \right )-\sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.813 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y+1 = \sin \left (x \right )+x +x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.04 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 18 \,{\mathrm e}^{-3 x}+8 \sin \left (x \right )+6 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.781 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+1 = 3 \sin \left (2 x \right )+\cos \left (x \right ) \] |
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]] |
✓ |
✓ |
3.422 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime } = 2 x +{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.169 |
|
|
\[ {}y^{\prime \prime }+y = 2 \sin \left (x \right ) \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.769 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime } = 4 x +3 \sin \left (x \right )+\cos \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.71 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = {\mathrm e}^{2 x} x +\sin \left (x \right )+x^{2} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.459 |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime \prime } = x \,{\mathrm e}^{x}-1 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.17 |
|
|
\[ {}y^{\left (5\right )}-y^{\prime \prime \prime } = x +2 \,{\mathrm e}^{-x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.174 |
|
|
\[ {}y^{\prime \prime }+y = 2-2 x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.507 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 9 x^{2}-12 x +2 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.638 |
|
|
\[ {}y^{\prime \prime }+9 y = 36 \,{\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.662 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.657 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = \left (12 x -7\right ) {\mathrm e}^{-x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.584 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = {\mathrm e}^{-x} \] |
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]] |
✓ |
✓ |
1.381 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 10 \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.787 |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.77 |
|
|
\[ {}y^{\prime \prime }+y = 4 x \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.681 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 x^{2} {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 16 \,{\mathrm e}^{-x}+9 x -6 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.668 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = -5 \,{\mathrm e}^{-x} \left (\cos \left (x \right )+\sin \left (x \right )\right ) \] |
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]] |
✓ |
✓ |
2.992 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.786 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = -2 x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.539 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
1.296 |
|
|
\[ {}y^{\prime \prime \prime }-y = 2 x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.396 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 8 \,{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
1.104 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.538 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 4 \cos \left (2 x \right )+\sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.633 |
|
|
\[ {}y^{\prime \prime }-y = 1 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.75 |
|
|
\[ {}y^{\prime \prime }-y = -2 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.386 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.413 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 8 \,{\mathrm e}^{x}+9 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.382 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-5 y = 1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✗ |
N/A |
0.471 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.661 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+4 \cos \left (2 x \right )\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.591 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = {\mathrm e}^{-x} \left (9 x^{2}+5 x -12\right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
N/A |
0.493 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.964 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = 0 \] |
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]] |
✓ |
✓ |
1.899 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y = 0 \] |
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_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.697 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.774 |
|
|
\[ {}\left (2+x \right )^{2} y^{\prime \prime }+3 \left (2+x \right ) y^{\prime }-3 y = 0 \] |
kovacic, second_order_change_of_variable_on_x_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.79 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y = 0 \] |
kovacic, second_order_change_of_variable_on_x_method_1, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.802 |
|
|
\[ {}x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime } = 0 \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.47 |
|
|
\[ {}x^{2} y^{\prime \prime \prime } = 2 y^{\prime } \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.345 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime } = 0 \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.564 |
|
|
\[ {}\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+y^{\prime } = 0 \] |
higher_order_missing_y |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.044 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = x \left (6-\ln \left (x \right )\right ) \] |
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]] |
✓ |
✓ |
3.521 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = \sin \left (\ln \left (x \right )\right ) \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.589 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }-3 y = -\frac {16 \ln \left (x \right )}{x} \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.35 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y = x^{2}-2 x +2 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.255 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{m} \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.67 |
|
|
|
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|
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