|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.44 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+25 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.476 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.623 |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.474 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.906 |
|
|
\[ {}y^{\prime \prime }-2 i y^{\prime }+3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.474 |
|
|
\[ {}y^{\prime \prime }-i y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.506 |
|
|
\[ {}y^{\prime \prime } = \left (-2+2 i \sqrt {3}\right ) y \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.022 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+9 y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.455 |
|
|
\[ {}x^{2} y^{\prime \prime }+7 x y^{\prime }+25 y = 0 \] |
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]] |
✓ |
✓ |
1.691 |
|
|
\[ {}\frac {x^{\prime \prime }}{2}+3 x^{\prime }+4 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.688 |
|
|
\[ {}3 x^{\prime \prime }+30 x^{\prime }+63 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.693 |
|
|
\[ {}x^{\prime \prime }+8 x^{\prime }+16 x = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.893 |
|
|
\[ {}2 x^{\prime \prime }+12 x^{\prime }+50 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.862 |
|
|
\[ {}4 x^{\prime \prime }+20 x^{\prime }+169 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.981 |
|
|
\[ {}2 x^{\prime \prime }+16 x^{\prime }+40 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.924 |
|
|
\[ {}x^{\prime \prime }+10 x^{\prime }+125 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.961 |
|
|
\[ {}y^{\prime \prime }+16 y = {\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 3 x +4 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.579 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 2 \sin \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.759 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 3 x \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.785 |
|
|
\[ {}2 y^{\prime \prime }+4 y^{\prime }+7 y = x^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.003 |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.197 |
|
|
\[ {}y^{\prime \prime }-4 y = \cosh \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.093 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 1+x \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.8 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 x \right )+3 \sin \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.103 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 x^{2} {\mathrm e}^{3 x}+5 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 x \cos \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.976 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = x \left ({\mathrm e}^{-x}-{\mathrm e}^{-2 x}\right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.869 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+13 y = x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.028 |
|
|
\[ {}y^{\prime \prime }+4 y = 2 x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.961 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.975 |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.267 |
|
|
\[ {}y^{\prime \prime }+y = \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.081 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 1+x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.989 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \sin \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.503 |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (x \right )^{4} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.718 |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right )^{3} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.723 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 4 \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.541 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-8 y = 3 \,{\mathrm e}^{-2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 2 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime \prime }-4 y = \sinh \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.061 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.715 |
|
|
\[ {}y^{\prime \prime }+9 y = \sin \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.756 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sec \left (3 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.964 |
|
|
\[ {}y^{\prime \prime }+y = \csc \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.841 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.084 |
|
|
\[ {}y^{\prime \prime }-4 y = x \,{\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.585 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 72 x^{5} \] |
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]] |
✓ |
✓ |
3.015 |
|
|
\[ {}x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y = x^{3} \] |
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 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.511 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = x^{4} \] |
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]] |
✓ |
✓ |
2.28 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-4 x y^{\prime }+3 y = 8 x^{\frac {4}{3}} \] |
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 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.498 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+y = \ln \left (x \right ) \] |
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]] |
✓ |
✓ |
6.312 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = x^{2}-1 \] |
kovacic, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.895 |
|
|
\[ {}x^{\prime \prime }+9 x = 10 \cos \left (2 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.181 |
|
|
\[ {}x^{\prime \prime }+4 x = 5 \sin \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.231 |
|
|
\[ {}x^{\prime \prime }+100 x = 225 \cos \left (5 t \right )+300 \sin \left (5 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.939 |
|
|
\[ {}x^{\prime \prime }+25 x = 90 \cos \left (4 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.28 |
|
|
\[ {}m x^{\prime \prime }+k x = F_{0} \cos \left (\omega t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.039 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+4 x = 10 \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.993 |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+5 x = -4 \cos \left (5 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.577 |
|
|
\[ {}2 x^{\prime \prime }+2 x^{\prime }+x = 3 \sin \left (10 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.009 |
|
|
\[ {}x^{\prime \prime }+3 x^{\prime }+3 x = 8 \cos \left (10 t \right )+6 \sin \left (10 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.528 |
|
|
\[ {}x^{\prime \prime }+4 x^{\prime }+5 x = 10 \cos \left (3 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.598 |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.824 |
|
|
\[ {}x^{\prime \prime }+6 x^{\prime }+13 x = 10 \sin \left (5 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.03 |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }+26 x = 600 \cos \left (10 t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.022 |
|
|
\[ {}x^{\prime \prime }+8 x^{\prime }+25 x = 200 \cos \left (t \right )+520 \sin \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.733 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 y \\ y^{\prime }=3 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.593 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-2 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.081 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+4 y+3 \,{\mathrm e}^{t} \\ y^{\prime }=5 x-y-t^{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.159 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y+z \\ y^{\prime }=z+x \\ z^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2} \\ x_{2}^{\prime }=2 x_{3} \\ x_{3}^{\prime }=3 x_{4} \\ x_{4}^{\prime }=4 x_{1} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.901 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3}+1 \\ x_{2}^{\prime }=x_{3}+x_{4}+t \\ x_{3}^{\prime }=x_{1}+x_{4}+t^{2} \\ x_{4}^{\prime }=x_{1}+x_{2}+t^{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
7.091 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.385 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.24 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.628 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-\left (2+x \right ) y^{\prime }+y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.624 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.609 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
0.595 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.702 |
|
|
\[ {}5 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.299 |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+16 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.394 |
|
|
\[ {}y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+3 y^{\prime \prime }-y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.116 |
|
|
\[ {}9 y^{\prime \prime \prime }+12 y^{\prime \prime }+4 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.438 |
|
|
\[ {}y^{\prime \prime \prime \prime }-16 y^{\prime \prime }+16 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.634 |
|
|
\[ {}y^{\prime \prime \prime \prime }+18 y^{\prime \prime }+81 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.141 |
|
|
\[ {}6 y^{\prime \prime \prime \prime }+11 y^{\prime \prime }+4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.583 |
|
|
\[ {}y^{\prime \prime \prime \prime } = 16 y \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.352 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.165 |
|
|
\[ {}2 y^{\prime \prime \prime }-3 y^{\prime \prime }-2 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.585 |
|
|
\[ {}3 y^{\prime \prime \prime }+2 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{\prime \prime \prime }+10 y^{\prime \prime }+25 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }-4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.365 |
|
|
\[ {}2 y^{\prime \prime \prime }-y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.309 |
|
|
|
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|
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