|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y \sin \left (\frac {t}{y}\right )-\left (t +t \sin \left (\frac {t}{y}\right )\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.586 |
|
|
\[ {}y^{\prime } = \frac {2 t^{5}}{5 y^{2}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.595 |
|
|
\[ {}\cos \left (4 x \right )-8 \sin \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.574 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
exact, riccati, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.98 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{8 y}}{t} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.113 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{5 t}}{y^{4}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.912 |
|
|
\[ {}-\frac {1}{x^{5}}+\frac {1}{x^{3}} = \left (2 y^{4}-6 y^{9}\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.445 |
|
|
\[ {}y^{\prime } = \frac {y \,{\mathrm e}^{-2 t}}{\ln \left (y\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.911 |
|
|
\[ {}y^{\prime } = \frac {\left (4-7 x \right ) \left (2 y-3\right )}{\left (-1+x \right ) \left (2 x -5\right )} \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.785 |
|
|
\[ {}y^{\prime }+3 y = -10 \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.303 |
|
|
\[ {}3 t +\left (t -4 y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.595 |
|
|
\[ {}y-t +\left (t +y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.921 |
|
|
\[ {}y-x +y^{\prime } = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.888 |
|
|
\[ {}y^{2}+\left (t y+t^{2}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.637 |
|
|
\[ {}r^{\prime } = \frac {r^{2}+t^{2}}{r t} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.603 |
|
|
\[ {}x^{\prime } = \frac {5 t x}{x^{2}+t^{2}} \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
5.543 |
|
|
\[ {}t^{2}-y+\left (-t +y\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.964 |
|
|
\[ {}t^{2} y+\sin \left (t \right )+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
9.555 |
|
|
\[ {}\tan \left (y\right )-t +\left (t \sec \left (y\right )^{2}+1\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
4.931 |
|
|
\[ {}t \ln \left (y\right )+\left (\frac {t^{2}}{2 y}+1\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.882 |
|
|
\[ {}y^{\prime }+y = 5 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.445 |
|
|
\[ {}y^{\prime }+t y = t \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.487 |
|
|
\[ {}x^{\prime }+\frac {x}{y} = y^{2} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.267 |
|
|
\[ {}t r^{\prime }+r = t \cos \left (t \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.18 |
|
|
\[ {}y^{\prime }-y = t y^{3} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.333 |
|
|
\[ {}y^{\prime }+y = \frac {{\mathrm e}^{t}}{y^{2}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
1.687 |
|
|
\[ {}y = t y^{\prime }+3 {y^{\prime }}^{4} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
2.53 |
|
|
\[ {}y-t y^{\prime } = 2 y^{2} \ln \left (t \right ) \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
1.624 |
|
|
\[ {}y-t y^{\prime } = -2 {y^{\prime }}^{3} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.726 |
|
|
\[ {}y-t y^{\prime } = -4 {y^{\prime }}^{2} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.48 |
|
|
\[ {}2 x -y-2+\left (2 y-x \right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
7.896 |
|
|
\[ {}\cos \left (t -y\right )+\left (1-\cos \left (t -y\right )\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
9.635 |
|
|
\[ {}{\mathrm e}^{t y} y-2 t +t \,{\mathrm e}^{t y} y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
2.181 |
|
|
\[ {}\sin \left (y\right )-y \cos \left (t \right )+\left (t \cos \left (y\right )-\sin \left (t \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
11.48 |
|
|
\[ {}y^{2}+\left (2 t y-2 \cos \left (y\right ) \sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.804 |
|
|
\[ {}\frac {y}{t}+\ln \left (y\right )+\left (\frac {t}{y}+\ln \left (t \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
3.188 |
|
|
\[ {}y^{\prime } = y^{2}-x \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
3.14 |
|
|
\[ {}y^{\prime } = \sqrt {x -y} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
7.889 |
|
|
\[ {}y^{\prime } = x +y^{\frac {1}{3}} \] |
unknown |
[_Chini] |
❇ |
N/A |
0.863 |
|
|
\[ {}y^{\prime } = \sin \left (x^{2} y\right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.079 |
|
|
\[ {}y^{\prime } = t y^{3} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.024 |
|
|
\[ {}y^{\prime } = \frac {t}{y^{3}} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.13 |
|
|
\[ {}y^{\prime } = -\frac {y}{t -2} \] |
exact, linear, separable, differentialType, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.637 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.292 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.381 |
|
|
\[ {}2 t^{2} y^{\prime \prime }-3 t y^{\prime }-3 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.671 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.941 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.305 |
|
|
\[ {}3 t^{2} y^{\prime \prime }-5 t y^{\prime }-3 y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.791 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }-7 y = 0 \] |
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]] |
✓ |
✓ |
4.243 |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.036 |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+24 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.322 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.914 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+18 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.708 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-y = 0 \] |
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]] |
✓ |
✓ |
3.97 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.283 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.286 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.441 |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.287 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.563 |
|
|
\[ {}y^{\prime \prime }+49 y = 0 \] |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.544 |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }-4 y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.521 |
|
|
\[ {}t^{2} y^{\prime \prime }+6 t y^{\prime }+6 y = 0 \] |
reduction_of_order |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.578 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-\frac {1}{4}\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.758 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
reduction_of_order |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.548 |
|
|
\[ {}a y^{\prime \prime }+b y^{\prime }+c y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.607 |
|
|
\[ {}t^{2} y^{\prime \prime }+a t y^{\prime }+b y = 0 \] |
kovacic, second_order_euler_ode, second_order_change_of_variable_on_x_method_2, second_order_change_of_variable_on_y_method_2 |
[[_Emden, _Fowler]] |
✓ |
✓ |
3.349 |
|
|
\[ {}4 t^{2} y^{\prime \prime }+4 t y^{\prime }+\left (36 t^{2}-1\right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.005 |
|
|
\[ {}t y^{\prime \prime }+2 y^{\prime }+16 t y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.822 |
|
|
\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.766 |
|
|
\[ {}y^{\prime \prime }+b \left (t \right ) y^{\prime }+c \left (t \right ) y = 0 \] |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.922 |
|
|
\[ {}y^{\prime \prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_quadrature, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
0.84 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }-12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.328 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
1.27 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.325 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }+12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.325 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.386 |
|
|
\[ {}8 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.342 |
|
|
\[ {}4 y^{\prime \prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.474 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.194 |
|
|
\[ {}y^{\prime \prime }+8 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.447 |
|
|
\[ {}y^{\prime \prime }+7 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.267 |
|
|
\[ {}4 y^{\prime \prime }+21 y^{\prime }+5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.344 |
|
|
\[ {}7 y^{\prime \prime }+4 y^{\prime }-3 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.339 |
|
|
\[ {}4 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.391 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.372 |
|
|
\[ {}y^{\prime \prime }-y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
1.337 |
|
|
\[ {}3 y^{\prime \prime }-y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.582 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.576 |
|
|
\[ {}2 y^{\prime \prime }-7 y^{\prime }-4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.596 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+10 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.545 |
|
|
\[ {}y^{\prime \prime }+36 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
8.265 |
|
|
\[ {}y^{\prime \prime }+100 y = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
14.04 |
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|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.674 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.761 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.9 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.975 |
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|
|
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