|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}2 x y^{2}+y+\left (2 y^{3}-x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[_rational] |
✓ |
✓ |
2.313 |
|
|
\[ {}4 x y^{2}+6 y+\left (5 x^{2} y+8 x \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.113 |
|
|
\[ {}8 x^{2} y^{3}-2 y^{4}+\left (5 x^{3} y^{2}-8 x y^{3}\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.99 |
|
|
\[ {}5 x +2 y+1+\left (y+2 x +1\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.466 |
|
|
\[ {}3 x -y+1-\left (6 x -2 y-3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.452 |
|
|
\[ {}x -2 y-3+\left (2 x +y-1\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.211 |
|
|
\[ {}10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.471 |
|
|
\[ {}6 x +4 y+1+\left (4 x +2 y+2\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
9.043 |
|
|
\[ {}3 x -y-6+\left (x +y+2\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.579 |
|
|
\[ {}2 x +3 y+1+\left (4 x +6 y+1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.896 |
|
|
\[ {}4 x +3 y+1+\left (1+x +y\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
13.358 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.758 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.18 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
unknown |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
1.577 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.265 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.569 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
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_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
3.202 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
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)]‘]] |
✓ |
✓ |
2.202 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.271 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.253 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }+8 x y^{\prime }-8 y = 0 \] |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.461 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+4 y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.471 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime \prime }-3 \left (1+x \right ) y^{\prime }+3 y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.588 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.613 |
|
|
\[ {}\left (x^{2}-x +1\right ) y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.006 |
|
|
\[ {}\left (2 x +1\right ) y^{\prime \prime }-4 \left (1+x \right ) y^{\prime }+4 y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.685 |
|
|
\[ {}\left (x^{3}-x^{2}\right ) y^{\prime \prime }-\left (x^{3}+2 x^{2}-2 x \right ) y^{\prime }+\left (2 x^{2}+2 x -2\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.828 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 4 x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.42 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2-12 x +6 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.501 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.279 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.285 |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.282 |
|
|
\[ {}3 y^{\prime \prime }-14 y^{\prime }-5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.31 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.232 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+5 y^{\prime }+12 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.237 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.336 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.342 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.665 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+25 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.802 |
|
|
\[ {}4 y^{\prime \prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.345 |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+7 y^{\prime }-3 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.292 |
|
|
\[ {}4 y^{\prime \prime \prime }+4 y^{\prime \prime }-7 y^{\prime }+2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.312 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.142 |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.647 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.333 |
|
|
\[ {}y^{\prime \prime \prime \prime }+8 y^{\prime \prime }+16 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.16 |
|
|
\[ {}y^{\left (5\right )}-2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-3 y^{\prime \prime }+y^{\prime }+2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.334 |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }-2 y^{\prime \prime }+2 y^{\prime }+12 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+15 y^{\prime \prime }+20 y^{\prime }+12 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.859 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
1.241 |
|
|
\[ {}y^{\left (5\right )} = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.227 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.536 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+8 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.5 |
|
|
\[ {}3 y^{\prime \prime }+4 y^{\prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.498 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.689 |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.688 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.716 |
|
|
\[ {}9 y^{\prime \prime }-6 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.661 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+29 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+58 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.927 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.89 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.859 |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.894 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+37 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.871 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.466 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.716 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.531 |
|
|
\[ {}y^{\prime \prime \prime }-5 y^{\prime \prime }+9 y^{\prime }-5 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.749 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+6 y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.702 |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }+13 y^{\prime }+30 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.479 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+8 y = 4 x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.038 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 4 \,{\mathrm e}^{2 x}-21 \,{\mathrm e}^{-3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.602 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 6 \sin \left (2 x \right )+7 \cos \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.03 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 10 \sin \left (4 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.043 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+4 y = \cos \left (4 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.674 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-4 y = 16 x -12 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = 2 \,{\mathrm e}^{x}+10 \,{\mathrm e}^{5 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.598 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 5 x \,{\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.924 |
|
|
\[ {}y^{\prime \prime \prime }+4 y^{\prime \prime }+y^{\prime }-6 y = -18 x^{2}+1 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.732 |
|
|
\[ {}y^{\prime \prime \prime }+2 y^{\prime \prime }-3 y^{\prime }-10 y = 8 x \,{\mathrm e}^{-2 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.954 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }+3 y^{\prime }-5 y = 5 \sin \left (2 x \right )+10 x^{2}+3 x +7 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
8.708 |
|
|
\[ {}4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y = 3 x^{3}-8 x \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.669 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 10 \,{\mathrm e}^{2 x}-18 \,{\mathrm e}^{3 x}-6 x -11 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.77 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 6 \,{\mathrm e}^{-2 x}+3 \,{\mathrm e}^{x}-4 x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.9 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y = 4 \,{\mathrm e}^{x}-18 \,{\mathrm e}^{-x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.786 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 9 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{3 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.624 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = 2 x^{2}+4 \sin \left (x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.989 |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 3 \,{\mathrm e}^{-x}+6 \,{\mathrm e}^{2 x}-6 x \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.333 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = x \,{\mathrm e}^{x}-4 \,{\mathrm e}^{2 x}+6 \,{\mathrm e}^{4 x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 3 x^{2} {\mathrm e}^{x}-7 \,{\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.709 |
|
|
\[ {}y^{\prime \prime }+y = x \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.943 |
|
|
\[ {}y^{\prime \prime }+4 y = 12 x^{2}-16 x \cos \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.52 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-3 y^{\prime \prime } = 18 x^{2}+16 x \,{\mathrm e}^{x}+4 \,{\mathrm e}^{3 x}-9 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_y]] |
✓ |
✓ |
0.377 |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+7 y^{\prime \prime }-5 y^{\prime }+6 y = 5 \sin \left (x \right )-12 \sin \left (2 x \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.107 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.733 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+4 y = 16 x +20 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.769 |
|
|
\[ {}y^{\prime \prime }-8 y^{\prime }+15 y = 9 \,{\mathrm e}^{2 x} x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.77 |
|
|
|
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