|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime \prime }+\frac {2 y^{\prime }}{2+x}+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.444 |
|
|
\[ {}4 y^{\prime \prime }+\frac {\left (4 x -3\right ) y}{\left (-1+x \right )^{2}} = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.477 |
|
|
\[ {}\left (x -3\right )^{2} y^{\prime \prime }+\left (x^{2}-3 x \right ) y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.636 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+\left (-x^{2}+2\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.257 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.482 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
0.997 |
|
|
\[ {}x^{2} \left (-x^{2}+2\right ) y^{\prime \prime }+\left (4 x^{2}+5 x \right ) y^{\prime }+\left (x^{2}+1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.926 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (2 x^{2}+5 x \right ) y^{\prime }+9 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.208 |
|
|
\[ {}x^{2} \left (2 x +1\right ) y^{\prime \prime }+x y^{\prime }+\left (4 x^{3}-4\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.866 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (1-4 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.211 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-\left (2 x +1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.799 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.595 |
|
|
\[ {}x y^{\prime \prime }+4 y^{\prime }+\frac {12 y}{\left (2+x \right )^{2}} = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.553 |
|
|
\[ {}\left (x -3\right ) y^{\prime \prime }+\left (x -3\right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.032 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.484 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (1-4 x \right ) y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.082 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x}+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
1.54 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x^{2}+x \right ) y^{\prime }+4 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
4.856 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (-4+4 x \right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.403 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=1-2 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.827 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=6 x-7 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.719 |
|
|
\[ {}\left [\begin {array}{c} t x^{\prime }+2 x=15 y \\ t y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✗ |
N/A |
0.042 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.712 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.627 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=3 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=5 x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=2 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.75 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=8 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.816 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.793 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.695 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=8 x+2 y-17 \\ y^{\prime }=4 x+y-13 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.019 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=8 x+2 y+7 \,{\mathrm e}^{2 t} \\ y^{\prime }=4 x+y-7 \,{\mathrm e}^{2 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+3 y-6 \,{\mathrm e}^{3 t} \\ y^{\prime }=x+6 y+2 \,{\mathrm e}^{3 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.15 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=4 x+24 t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.218 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-13 y \\ y^{\prime }=x+19 \cos \left (4 t \right )-13 \sin \left (4 t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.619 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+3 y+5 \operatorname {Heaviside}\left (t -2\right ) \\ y^{\prime }=x+6 y+17 \operatorname {Heaviside}\left (t -2\right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.465 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=8 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-5 y \\ y^{\prime }=3 x-7 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.059 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-5 y+4 \\ y^{\prime }=3 x-7 y+5 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.147 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=6 x+2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.67 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x y-6 y \\ y^{\prime }=x-y-5 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.257 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = x^{3} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.791 |
|
|
\[ {}y y^{\prime }+y^{4} = \sin \left (x \right ) \] |
unknown |
[‘y=_G(x,y’)‘] |
✗ |
N/A |
2.337 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime }+5 y^{\prime }+y = {\mathrm e}^{x} \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
68.348 |
|
|
\[ {}{y^{\prime }}^{2}+y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.197 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
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)]‘]] |
✓ |
✓ |
2.947 |
|
|
\[ {}x {y^{\prime \prime }}^{2}+2 y = 2 x \] |
unknown |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.493 |
|
|
\[ {}x^{\prime \prime }+2 \sin \left (x\right ) = \sin \left (2 t \right ) \] |
unknown |
[NONE] |
❇ |
N/A |
1.274 |
|
|
\[ {}2 x -1-y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.236 |
|
|
\[ {}2 x -y-y y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.731 |
|
|
\[ {}y^{\prime }+2 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.618 |
|
|
\[ {}y^{\prime }+x y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.553 |
|
|
\[ {}y^{\prime }+y = \sin \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.62 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
1.816 |
|
|
\[ {}x^{\prime \prime }+2 x^{\prime }-10 x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.527 |
|
|
\[ {}x^{\prime \prime }+x = t \cos \left (t \right )-\cos \left (t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.711 |
|
|
\[ {}y^{\prime \prime }-12 y^{\prime }+40 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.353 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.351 |
|
|
\[ {}x^{2} y^{\prime \prime }-12 x y^{\prime }+42 y = 0 \] |
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_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.977 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+5 y = 0 \] |
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]] |
✓ |
✓ |
2.825 |
|
|
\[ {}y^{\prime } = -\frac {x}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.871 |
|
|
\[ {}3 y \left (t^{2}+y\right )+t \left (t^{2}+6 y\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
4.441 |
|
|
\[ {}y^{\prime } = -\frac {2 y}{x}-3 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.029 |
|
|
\[ {}y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.627 |
|
|
\[ {}\frac {y}{x}+\cos \left (y\right )+\left (\ln \left (x \right )-x \sin \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
5.138 |
|
|
\[ {}y^{\prime } = \left (x^{2}-1\right ) \left (x^{3}-3 x \right )^{3} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.47 |
|
|
\[ {}y^{\prime } = x \sin \left (x^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.158 |
|
|
\[ {}y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.473 |
|
|
\[ {}y^{\prime } = \frac {1}{x \ln \left (x \right )} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.248 |
|
|
\[ {}y^{\prime } = x \ln \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.255 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{-x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.314 |
|
|
\[ {}y^{\prime } = \frac {-2 x -10}{\left (2+x \right ) \left (x -4\right )} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.416 |
|
|
\[ {}y^{\prime } = \frac {-x^{2}+x}{\left (1+x \right ) \left (x^{2}+1\right )} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.508 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {x^{2}-16}}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.862 |
|
|
\[ {}y^{\prime } = \left (-x^{2}+4\right )^{\frac {3}{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.289 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}-16} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.33 |
|
|
\[ {}y^{\prime } = \cos \left (x \right ) \cot \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.217 |
|
|
\[ {}y^{\prime } = \sin \left (x \right )^{3} \tan \left (x \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.884 |
|
|
\[ {}y^{\prime }+2 y = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.752 |
|
|
\[ {}y^{\prime }+y = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.041 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.905 |
|
|
\[ {}y^{\prime \prime }+9 y^{\prime } = 0 \] |
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]] |
✓ |
✓ |
2.472 |
|
|
\[ {}y^{\prime \prime \prime }-2 y^{\prime \prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.709 |
|
|
\[ {}y^{\prime \prime \prime }-4 y^{\prime } = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.779 |
|
|
\[ {}t^{2} y^{\prime \prime }-12 t y^{\prime }+42 y = 0 \] |
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_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.648 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = 0 \] |
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]] |
✓ |
✓ |
5.391 |
|
|
\[ {}y^{\prime } = 4 x^{3}-x +2 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.502 |
|
|
\[ {}y^{\prime } = \sin \left (2 t \right )-\cos \left (2 t \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.24 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (\frac {1}{x}\right )}{x^{2}} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.26 |
|
|
\[ {}y^{\prime } = \frac {\ln \left (x \right )}{x} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.608 |
|
|
\[ {}y^{\prime } = \frac {\left (x -4\right ) y^{3}}{x^{3} \left (y-2\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.083 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+2 x y}{x^{2}} \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.803 |
|
|
\[ {}x y^{\prime }+y = \cos \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.547 |
|
|
\[ {}16 y^{\prime \prime }+24 y^{\prime }+153 y = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.883 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 y \\ y^{\prime }=-x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.799 |
|
|
\[ {}4 x \left (x^{2}+y^{2}\right )-5 y+4 y \left (x^{2}+y^{2}-5 x \right ) y^{\prime } = 0 \] |
unknown |
[_rational] |
❇ |
N/A |
31.028 |
|
|
|
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