|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.826 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.66 |
|
|
\[ {}y^{\prime \prime }+12 y = 7 y^{\prime } \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.283 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.327 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.424 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.324 |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.328 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.439 |
|
|
\[ {}y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.305 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.244 |
|
|
\[ {}y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.154 |
|
|
\[ {}y^{\left (5\right )}-4 y^{\prime \prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.276 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime }+9 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.745 |
|
|
\[ {}y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.362 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.596 |
|
|
\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.177 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = x \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.388 |
|
|
\[ {}s^{\prime \prime }-a^{2} s = t +1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.515 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 8 \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }-y = 5 x +2 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.397 |
|
|
\[ {}y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.521 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+5 y = {\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.398 |
|
|
\[ {}y^{\prime \prime }+9 y = 6 \,{\mathrm e}^{3 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime } = 2-6 x \] |
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]] |
✓ |
✓ |
1.148 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+3 y = {\mathrm e}^{-x} \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.955 |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.604 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y = 2 x +3 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.585 |
|
|
\[ {}y^{\prime \prime \prime \prime }-a^{4} y = 5 a^{4} {\mathrm e}^{x a} \sin \left (x a \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.258 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 8 \cos \left (x a \right ) \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.906 |
|
|
\[ {}y^{\prime \prime }+2 h y^{\prime }+n^{2} y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.816 |
|
|
\[ {}y^{\prime \prime }+n^{2} y = h \sin \left (r x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.307 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+6 y = \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.477 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime \prime }+y = \frac {1}{\cos \left (2 x \right )^{\frac {3}{2}}} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.885 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y+1 \\ y^{\prime }=1+x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.499 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.275 |
|
|
\[ {}\left [\begin {array}{c} 4 x^{\prime }-y^{\prime }+3 x=\sin \left (t \right ) \\ x^{\prime }+y=\cos \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.961 |
|
|
\[ {}y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
3.893 |
|
|
\[ {}\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}} = 0 \] |
exact, riccati, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.8 |
|
|
\[ {}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2} \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.393 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.435 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }-x y-\alpha = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.156 |
|
|
\[ {}x \cos \left (\frac {y}{x}\right ) y^{\prime } = y \cos \left (\frac {y}{x}\right )-x \] |
homogeneousTypeD, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.165 |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 x} \sin \left (2 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.616 |
|
|
\[ {}x y^{\prime }+y-y^{2} \ln \left (x \right ) = 0 \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.868 |
|
|
\[ {}2 x +2 y-1+\left (x +y-2\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.849 |
|
|
\[ {}3 \,{\mathrm e}^{x} \tan \left (y\right )+\left (-{\mathrm e}^{x}+1\right ) \sec \left (y\right )^{2} y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.802 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-3 y \\ y^{\prime }=5 x+6 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.704 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-10 y \\ y^{\prime }=x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.426 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=12 x+18 y \\ y^{\prime }=-8 x-12 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.224 |
|
|
\[ {}y^{\prime } = x +y^{2} \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
4.751 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = {\mathrm e}^{x} \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.924 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=-x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.322 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.38 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+2 y \\ y^{\prime }=3 x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.448 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=2 x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.432 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=3 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.287 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.66 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.288 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=2 x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.262 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.255 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.242 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=2 x-4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.428 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.218 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.186 |
|
|
\[ {}x^{\prime \prime }+x-x^{3} = 0 \] |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
2.03 |
|
|
\[ {}x^{\prime \prime }+x+x^{3} = 0 \] |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], _Duffing, [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
1.734 |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x-x^{3} = 0 \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x]] |
❇ |
N/A |
0.488 |
|
|
\[ {}x^{\prime \prime }+x^{\prime }+x+x^{3} = 0 \] |
second_order_ode_missing_x |
[[_2nd_order, _missing_x]] |
❇ |
N/A |
0.491 |
|
|
\[ {}x^{\prime \prime } = \left (2 \cos \left (x\right )-1\right ) \sin \left (x\right ) \] |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
85.822 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-5 y \\ y^{\prime }=x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.387 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
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]] |
✓ |
✓ |
1.733 |
|
|
\[ {}-y+x y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.635 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+3 x y^{\prime }-y = 0 \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.487 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.287 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 y = 0 \] |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.987 |
|
|
\[ {}y^{\prime }+\frac {1}{2 y} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.3 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = 1 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.638 |
|
|
\[ {}y^{\prime }-2 \sqrt {{| y|}} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.026 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.812 |
|
|
\[ {}y^{\prime }-y^{2} = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.214 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
kovacic, second_order_euler_ode, 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]] |
✓ |
✓ |
1.102 |
|
|
\[ {}x y^{\prime }-\sin \left (x \right ) = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.306 |
|
|
\[ {}y^{\prime }+3 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.274 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }-10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.276 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.337 |
|
|
\[ {}y^{\prime \prime \prime }-7 y^{\prime \prime }+12 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.266 |
|
|
\[ {}2 x y^{\prime }-y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.7 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime } = 0 \] |
kovacic, second_order_euler_ode, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.579 |
|
|
\[ {}x^{2} y^{\prime \prime }+6 x y^{\prime }+4 y = 0 \] |
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]] |
✓ |
✓ |
1.641 |
|
|
\[ {}x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y = 0 \] |
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]] |
✓ |
✓ |
1.111 |
|
|
\[ {}{y^{\prime }}^{2}-4 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.437 |
|
|
\[ {}{y^{\prime }}^{2}-9 x y = 0 \] |
first_order_nonlinear_p_but_separable |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
0.653 |
|
|
\[ {}{y^{\prime }}^{2} = x^{6} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.417 |
|
|
\[ {}y^{\prime }-2 x y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime }+y = x^{2}+2 x -1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.628 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.291 |
|
|
\[ {}y^{\prime } = x \sqrt {y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.558 |
|
|
|
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