|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}x \left (-2+x \right )^{2} y^{\prime \prime }-2 \left (-2+x \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.595 |
|
|
\[ {}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.388 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.366 |
|
|
\[ {}x y^{\prime \prime }-\left (2+x \right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
2.484 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.95 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (x +5\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.242 |
|
|
\[ {}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.961 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-10 x y^{\prime }-18 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.44 |
|
|
\[ {}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.214 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-8 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_erf] |
✓ |
✓ |
0.324 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.112 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.223 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-2 x \left (2+x \right ) y^{\prime }+\left (x +3\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.056 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.429 |
|
|
\[ {}2 x y^{\prime \prime }+y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.924 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.306 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.582 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.628 |
|
|
\[ {}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.402 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.023 |
|
|
\[ {}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.531 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.02 |
|
|
\[ {}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.937 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.567 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (x^{2}+4\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Bessel, _modified]] |
✓ |
✓ |
2.235 |
|
|
\[ {}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (2+x \right ) y^{\prime }+18 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.143 |
|
|
\[ {}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.898 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y \left (1+x \right ) = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.473 |
|
|
\[ {}y^{\prime } = \frac {y}{x \ln \left (x \right )} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.048 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 5 x^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.654 |
|
|
\[ {}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.777 |
|
|
\[ {}y^{\prime } = \frac {2 x -y}{x +4 y} \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.537 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x} = 6 x^{4} y^{2} \] |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{2}+\cos \left (x \right )+\left (2 x y+\sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
0.425 |
|
|
\[ {}x y-1+x^{2} y^{\prime } = 0 \] |
exact |
[_linear] |
✓ |
✓ |
0.302 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.607 |
|
|
\[ {}y^{\prime \prime }+16 y = 4 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.9 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+3 y = 9 x^{2}+4 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.808 |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right )^{2} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.883 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=-2 x+5 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.421 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+4 y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.427 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+2 y+4 \,{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.872 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=6 x-7 y+10 \\ y^{\prime }=x-2 y-2 \,{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.278 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (y\right ) \sec \left (x \right )}{x} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.487 |
|
|
\[ {}y^{\prime } = x \left (\cos \left (y\right )+y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.819 |
|
|
\[ {}y^{\prime } = \frac {\sec \left (x \right ) \left (\sin \left (y\right )+y\right )}{x} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.619 |
|
|
\[ {}y^{\prime } = \left (5+\frac {\sec \left (x \right )}{x}\right ) \left (\sin \left (y\right )+y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
11.605 |
|
|
\[ {}y^{\prime } = y+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.175 |
|
|
\[ {}y^{\prime } = 1+x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.108 |
|
|
\[ {}y^{\prime } = x \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.092 |
|
|
\[ {}y^{\prime } = y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.103 |
|
|
\[ {}y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.072 |
|
|
\[ {}y^{\prime } = 1+\frac {\sec \left (x \right )}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.217 |
|
|
\[ {}y^{\prime } = x +\frac {\sec \left (x \right ) y}{x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.544 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.577 |
|
|
\[ {}y^{\prime } = \frac {\ln \left (1+y^{2}\right )}{\ln \left (x^{2}+1\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.029 |
|
|
\[ {}y^{\prime } = \frac {1}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.096 |
|
|
\[ {}y^{\prime } = \frac {-x y-1}{4 x^{3} y-2 x^{2}} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.513 |
|
|
\[ {}\frac {{y^{\prime }}^{2}}{4}-x y^{\prime }+y = 0 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.258 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y+1}{y^{2}}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
48.819 |
|
|
\[ {}y^{\prime } = \sqrt {1-x^{2}-y^{2}} \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
0.629 |
|
|
\[ {}y^{\prime }+\frac {y}{3} = \frac {\left (1-2 x \right ) y^{4}}{3} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
1.113 |
|
|
\[ {}y^{\prime } = \sqrt {y}+x \] |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _Chini] |
✓ |
✓ |
3.674 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = x y y^{\prime } \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.532 |
|
|
\[ {}y = x y^{\prime }+x^{2} {y^{\prime }}^{2} \] |
separable |
[_separable] |
✓ |
✓ |
2.337 |
|
|
\[ {}\left (x +y\right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.107 |
|
|
\[ {}x y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.069 |
|
|
\[ {}\frac {y^{\prime }}{x +y} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.071 |
|
|
\[ {}\frac {y^{\prime }}{x} = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.069 |
|
|
\[ {}y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.068 |
|
|
\[ {}y = x {y^{\prime }}^{2}+{y^{\prime }}^{2} \] |
dAlembert |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
0.378 |
|
|
\[ {}y^{\prime } = \frac {5 x^{2}-x y+y^{2}}{x^{2}} \] |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
2.058 |
|
|
\[ {}2 t +3 x+\left (x+2\right ) x^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.444 |
|
|
\[ {}y^{\prime } = \frac {1}{1-y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.278 |
|
|
\[ {}p^{\prime } = a p-b p^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.123 |
|
|
\[ {}y^{2}+\frac {2}{x}+2 x y y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
0.987 |
|
|
\[ {}x f^{\prime }-f = \frac {{f^{\prime }}^{2} \left (1-{f^{\prime }}^{\lambda }\right )^{2}}{\lambda ^{2}} \] |
clairaut |
[_Clairaut] |
✓ |
✓ |
41.631 |
|
|
\[ {}x y^{\prime }-2 y+b y^{2} = c \,x^{4} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
1.987 |
|
|
\[ {}x y^{\prime }-y+y^{2} = x^{\frac {2}{3}} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
22.616 |
|
|
\[ {}u^{\prime }+u^{2} = \frac {1}{x^{\frac {4}{5}}} \] |
riccati |
[_rational, _Riccati] |
✓ |
✓ |
0.265 |
|
|
\[ {}y y^{\prime }-y = x \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.423 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.323 |
|
|
\[ {}5 y^{\prime \prime }+2 y^{\prime }+4 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.092 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = 1 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.799 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+4 y = \sin \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.089 |
|
|
\[ {}y = x {y^{\prime }}^{2} \] |
dAlembert, first_order_nonlinear_p_but_separable |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.881 |
|
|
\[ {}y y^{\prime } = 1-x {y^{\prime }}^{3} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
152.454 |
|
|
\[ {}f^{\prime } = \frac {1}{f} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.257 |
|
|
\[ {}t y^{\prime \prime }+4 y^{\prime } = t^{2} \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.355 |
|
|
\[ {}\left (t^{2}+9\right ) y^{\prime \prime }+2 t y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
2.044 |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+5 y = 0 \] |
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]] |
✓ |
✓ |
2.004 |
|
|
\[ {}t y^{\prime \prime }+y^{\prime } = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.972 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y^{\prime } = 0 \] |
kovacic, second_order_ode_missing_y, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime \prime }+\frac {\left (t^{2}-1\right ) y^{\prime }}{t}+\frac {t^{2} y}{\left (1+{\mathrm e}^{\frac {t^{2}}{2}}\right )^{2}} = 0 \] |
unknown |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
N/A |
2.566 |
|
|
\[ {}t y^{\prime \prime }-y^{\prime }+4 t^{3} y = 0 \] |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.806 |
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\[ {}y^{\prime \prime } = 0 \] |
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]] |
✓ |
✓ |
0.726 |
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\[ {}y^{\prime \prime } = 1 \] |
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]] |
✓ |
✓ |
1.167 |
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\[ {}y^{\prime \prime } = f \left (t \right ) \] |
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 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
1.664 |
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