|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x^{4} y^{\prime \prime }+x y^{\prime }+y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.415 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2 x^{2}+x \right ) y^{\prime }-4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.881 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.914 |
|
|
\[ {}\left (4 x^{3}-14 x^{2}-2 x \right ) y^{\prime \prime }-\left (6 x^{2}-7 x +1\right ) y^{\prime }+\left (6 x -1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.116 |
|
|
\[ {}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.833 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (-2+x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.793 |
|
|
\[ {}x^{2} \left (1-4 x \right ) y^{\prime \prime }+\left (\left (-n +1\right ) x -\left (6-4 n \right ) x^{2}\right ) y^{\prime }+n \left (-n +1\right ) x y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.455 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.021 |
|
|
\[ {}\left (a^{2}+x^{2}\right ) y^{\prime \prime }+x y^{\prime }-n^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.938 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+a^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.93 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.833 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+p x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.644 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.99 |
|
|
\[ {}x^{3} y^{\prime \prime }-\left (2 x -1\right ) y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.423 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1+x \right ) y^{\prime }+\left (3 x -1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.419 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.274 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-3 x^{2}+1\right ) y^{\prime }-x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_elliptic, _class_I]] |
✓ |
✓ |
0.84 |
|
|
\[ {}y^{\prime \prime }+\frac {a y}{x^{\frac {3}{2}}} = 0 \] |
second order series method. Irregular singular point |
[[_Emden, _Fowler]] |
❇ |
N/A |
0.148 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+4 x \right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.307 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_elliptic, _class_II]] |
✓ |
✓ |
1.324 |
|
|
\[ {}4 x \left (1-x \right ) y^{\prime \prime }-4 y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Jacobi] |
✓ |
✓ |
1.45 |
|
|
\[ {}x^{3} y^{\prime \prime }+y = x^{\frac {3}{2}} \] |
second order series method. Irregular singular point |
[[_2nd_order, _linear, _nonhomogeneous]] |
❇ |
N/A |
0.134 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-\left (3 x +2\right ) y^{\prime }+\frac {\left (2 x -1\right ) y}{x} = \sqrt {x} \] |
second order series method. Irregular singular point |
[[_2nd_order, _linear, _nonhomogeneous]] |
❇ |
N/A |
0.521 |
|
|
\[ {}\left (-x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }+2 y = 3 x^{2} \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.829 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }-\frac {y}{4} = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
0.981 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.099 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-11 x \right ) y^{\prime }-10 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
0.976 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\frac {\left (1-2 x \right ) y^{\prime }}{3}+\frac {20 y}{9} = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
1.019 |
|
|
\[ {}2 x \left (1-x \right ) y^{\prime \prime }+y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.936 |
|
|
\[ {}4 y^{\prime \prime }+\frac {3 \left (-x^{2}+2\right ) y}{\left (-x^{2}+1\right )^{2}} = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.851 |
|
|
\[ {}y^{2}+y^{\prime } = \frac {a^{2}}{x^{4}} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[_rational, _Riccati] |
✓ |
✓ |
1.376 |
|
|
\[ {}u^{\prime \prime }-\frac {a^{2} u}{x^{\frac {2}{3}}} = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.125 |
|
|
\[ {}u^{\prime \prime }-\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.504 |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}-a^{2} u = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.842 |
|
|
\[ {}u^{\prime \prime }+\frac {2 u^{\prime }}{x}+a^{2} u = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.53 |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}-a^{2} u = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.526 |
|
|
\[ {}u^{\prime \prime }+\frac {4 u^{\prime }}{x}+a^{2} u = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.727 |
|
|
\[ {}y^{\prime \prime }-a^{2} y = \frac {6 y}{x^{2}} \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.542 |
|
|
\[ {}y^{\prime \prime }+n^{2} y = \frac {6 y}{x^{2}} \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.81 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+\frac {1}{4}\right ) y = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.51 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\frac {\left (-9 a^{2}+4 x^{2}\right ) y}{4 a^{2}} = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.871 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {25}{4}\right ) y = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime \prime }+q y^{\prime } = \frac {2 y}{x^{2}} \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.484 |
|
|
\[ {}y^{\prime \prime }+{\mathrm e}^{2 x} y = n^{2} y \] |
second_order_bessel_ode_form_A |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.094 |
|
|
\[ {}y^{\prime \prime }+\frac {y}{4 x} = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.22 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime }+y = 0 \] |
second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.249 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime }+4 x^{3} y = 0 \] |
kovacic, second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.524 |
|
|
\[ {}y^{\prime } = y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.124 |
|
|
\[ {}x y^{\prime } = y \] |
separable |
[_separable] |
✓ |
✓ |
0.3 |
|
|
\[ {}x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.746 |
|
|
\[ {}y^{\prime } \sin \left (x \right ) = y \ln \left (y\right ) \] |
separable |
[_separable] |
✓ |
✓ |
2.048 |
|
|
\[ {}1+y^{2}+x y y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.519 |
|
|
\[ {}x y y^{\prime }-x y = y \] |
separable |
[_quadrature] |
✓ |
✓ |
0.375 |
|
|
\[ {}y^{\prime } = \frac {2 x y^{2}+x}{x^{2} y-y} \] |
separable |
[_separable] |
✓ |
✓ |
1.046 |
|
|
\[ {}y y^{\prime }+x y^{2}-8 x = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.517 |
|
|
\[ {}y^{\prime }+2 x y^{2} = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.279 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = y \] |
separable |
[_quadrature] |
✓ |
✓ |
0.387 |
|
|
\[ {}y^{\prime }-x y = x \] |
separable |
[_separable] |
✓ |
✓ |
0.321 |
|
|
\[ {}2 y^{\prime } = 3 \left (y-2\right )^{\frac {1}{3}} \] |
separable |
[_quadrature] |
✓ |
✓ |
0.264 |
|
|
\[ {}\left (x +x y\right ) y^{\prime }+y = 0 \] |
separable |
[_separable] |
✓ |
✓ |
2.856 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{x} \] |
linear |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.201 |
|
|
\[ {}x^{2} y^{\prime }+3 x y = 1 \] |
linear |
[_linear] |
✓ |
✓ |
0.173 |
|
|
\[ {}y^{\prime }+2 x y-x \,{\mathrm e}^{-x^{2}} = 0 \] |
linear |
[_linear] |
✓ |
✓ |
0.192 |
|
|
\[ {}2 x y^{\prime }+y = 2 x^{\frac {5}{2}} \] |
linear |
[_linear] |
✓ |
✓ |
0.275 |
|
|
\[ {}\cos \left (x \right ) y^{\prime }+y = \cos \left (x \right )^{2} \] |
linear |
[_linear] |
✓ |
✓ |
0.316 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {x^{2}+1}} = \frac {1}{x +\sqrt {x^{2}+1}} \] |
linear |
[_linear] |
✓ |
✓ |
0.214 |
|
|
\[ {}\left (1+{\mathrm e}^{x}\right ) y^{\prime }+2 \,{\mathrm e}^{x} y = \left (1+{\mathrm e}^{x}\right ) {\mathrm e}^{x} \] |
linear |
[_linear] |
✓ |
✓ |
0.2 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime }+y = \ln \left (x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.184 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime } = x y+2 x \sqrt {-x^{2}+1} \] |
linear |
[_linear] |
✓ |
✓ |
0.214 |
|
|
\[ {}y^{\prime }+y \tanh \left (x \right ) = 2 \,{\mathrm e}^{x} \] |
linear |
[_linear] |
✓ |
✓ |
0.206 |
|
|
\[ {}y^{\prime }+y \cos \left (x \right ) = \sin \left (2 x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.217 |
|
|
\[ {}x^{\prime } = \cos \left (y \right )-x \tan \left (y \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.175 |
|
|
\[ {}x^{\prime }+x-{\mathrm e}^{y} = 0 \] |
linear |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.164 |
|
|
\[ {}x^{\prime } = \frac {3 y^{\frac {2}{3}}-x}{3 y} \] |
linear |
[_linear] |
✓ |
✓ |
0.156 |
|
|
\[ {}y^{\prime }+y = x y^{\frac {2}{3}} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.57 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = 2 x^{\frac {3}{2}} \sqrt {y} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
3.696 |
|
|
\[ {}3 x y^{2} y^{\prime }+3 y^{3} = 1 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.345 |
|
|
\[ {}2 x \,{\mathrm e}^{3 y}+{\mathrm e}^{x}+\left (3 x^{2} {\mathrm e}^{3 y}-y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
1.407 |
|
|
\[ {}\left (x -y\right ) y^{\prime }+1+x +y = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.817 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )+\sin \left (x \right )^{2}-\left (\sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right )^{2}\right ) y^{\prime } = 0 \] |
exact |
unknown |
✓ |
✓ |
34.924 |
|
|
\[ {}x^{2} y^{\prime }+y^{2}-x y = 0 \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.135 |
|
|
\[ {}y y^{\prime } = -x +\sqrt {x^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.135 |
|
|
\[ {}x y+\left (-x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.023 |
|
|
\[ {}y^{2}-x y+\left (x y+x^{2}\right ) y^{\prime } = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.007 |
|
|
\[ {}y^{\prime } = \cos \left (x +y\right ) \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{\prime } = \frac {y}{x}-\tan \left (\frac {y}{x}\right ) \] |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.213 |
|
|
\[ {}\left (-1+x \right ) y^{\prime }+y-\frac {1}{x^{2}}+\frac {2}{x^{3}} = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.739 |
|
|
\[ {}y^{\prime } = x y^{2}-\frac {2 y}{x}-\frac {1}{x^{3}} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
1.128 |
|
|
\[ {}y^{\prime } = \frac {2 y^{2}}{x}+\frac {y}{x}-2 x \] |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.372 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-x} y^{2}+y-{\mathrm e}^{x} \] |
riccati, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _Riccati] |
✓ |
✓ |
0.921 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.303 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.319 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.721 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.316 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.353 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.668 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.285 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
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0.713 |
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\[ {}y^{\prime \prime }-4 y^{\prime }+13 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
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0.332 |
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\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
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✓ |
0.287 |
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