|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.602 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-x^{2} y^{\prime }+3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 y^{\prime }-x y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
0.53 |
|
|
\[ {}\left (x^{2}-2\right ) y^{\prime \prime }+2 y^{\prime }+y \sin \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.434 |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+3 y^{\prime }-6 x y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.754 |
|
|
\[ {}\left (t^{2}-t -2\right ) x^{\prime \prime }+\left (t +1\right ) x^{\prime }-\left (t -2\right ) x = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.035 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (1-x \right ) y^{\prime }+\left (x^{2}-2 x +1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.827 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }+y \cos \left (x \right ) = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.543 |
|
|
\[ {}{\mathrm e}^{x} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+2 x y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.792 |
|
|
\[ {}\sin \left (x \right ) y^{\prime \prime }-y \ln \left (x \right ) = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
4.331 |
|
|
\[ {}y^{\prime }+\left (2+x \right ) y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.401 |
|
|
\[ {}y^{\prime }-y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.368 |
|
|
\[ {}z^{\prime }-x^{2} z = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.358 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.489 |
|
|
\[ {}y^{\prime \prime }+\left (-1+x \right ) y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.652 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.497 |
|
|
\[ {}w^{\prime \prime }-x^{2} w^{\prime }+w = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Lienard] |
✓ |
✓ |
0.769 |
|
|
\[ {}\left (2 x -3\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.852 |
|
|
\[ {}\left (1+x \right ) y^{\prime \prime }-3 x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.993 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Hermite] |
✓ |
✓ |
0.798 |
|
|
\[ {}\left (x^{2}+x +1\right ) y^{\prime \prime }-3 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.342 |
|
|
\[ {}\left (x^{2}-5 x +6\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.8 |
|
|
\[ {}y^{\prime \prime }-\tan \left (x \right ) y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Lienard] |
✓ |
✓ |
2.783 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }-x y^{\prime }+2 x^{2} y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.335 |
|
|
\[ {}y^{\prime }+2 \left (-1+x \right ) y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.348 |
|
|
\[ {}y^{\prime }-2 x y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.415 |
|
|
\[ {}\left (x^{2}-2 x \right ) y^{\prime \prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.675 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+2 y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.786 |
|
|
\[ {}x^{2} y^{\prime \prime }-y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.814 |
|
|
\[ {}y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }-y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.793 |
|
|
\[ {}x^{\prime }+\sin \left (t \right ) x = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
2.027 |
|
|
\[ {}y^{\prime }-{\mathrm e}^{x} y = 0 \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.951 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-{\mathrm e}^{x} y^{\prime }+y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.539 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+y \,{\mathrm e}^{t} = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.905 |
|
|
\[ {}y^{\prime \prime }-{\mathrm e}^{2 x} y^{\prime }+y \cos \left (x \right ) = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.862 |
|
|
\[ {}y^{\prime }-x y = \sin \left (x \right ) \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_linear] |
✓ |
✓ |
0.528 |
|
|
\[ {}w^{\prime }+w x = {\mathrm e}^{x} \] |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_linear] |
✓ |
✓ |
0.481 |
|
|
\[ {}z^{\prime \prime }+x z^{\prime }+z = x^{2}+2 x +1 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+3 y = x^{2} \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.539 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = \cos \left (x \right ) \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.856 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+2 y = \cos \left (x \right ) \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.188 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime }+y = \tan \left (x \right ) \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.117 |
|
|
\[ {}y^{\prime \prime }-y \sin \left (x \right ) = \cos \left (x \right ) \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.561 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+n \left (n +1\right ) y = 0 \] |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
0.91 |
|
|
\[ {}x^{\prime \prime }-\omega ^{2} x = 0 \] |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.794 |
|
|
\[ {}x^{\prime \prime \prime }-x^{\prime \prime }+x^{\prime }-x = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.27 |
|
|
\[ {}x^{\prime \prime }+42 x^{\prime }+x = 0 \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.707 |
|
|
\[ {}x^{\prime \prime \prime \prime }+x = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.588 |
|
|
\[ {}x^{\prime \prime \prime }-3 x^{\prime \prime }-9 x^{\prime }-5 x = 0 \] |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.274 |
|
|
\[ {}x^{\prime \prime }+2 \gamma x^{\prime }+\omega _{0} x = F \cos \left (\omega t \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.78 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = {\mathrm e}^{2 x} \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.086 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 \cos \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.141 |
|
|
\[ {}y^{\prime \prime }+16 y = 16 \cos \left (4 x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime \prime }-y = \cosh \left (x \right ) \] |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.301 |
|
|
\[ {}y^{\prime }-y = {\mathrm e}^{2 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.553 |
|
|
\[ {}x^{2} y^{\prime }+2 x y-x +1 = 0 \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.41 |
|
|
\[ {}y^{\prime }+y = \left (1+x \right )^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.194 |
|
|
\[ {}x^{2} y^{\prime }+2 x y = \sinh \left (x \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.306 |
|
|
\[ {}y^{\prime }+\frac {y}{1-x}+2 x -x^{2} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime }+\frac {y}{1-x}+x -x^{2} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.593 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x y+1 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime }+x y = x y^{2} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.536 |
|
|
\[ {}3 x y^{\prime }+y+y^{4} x^{2} = 0 \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.913 |
|
|
\[ {}x \left (1+x \right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+\left (-1+x \right ) y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.64 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-2 x \right ) y^{\prime }-2 y = 0 \] |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.774 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-9 y = 0 \] |
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], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.366 |
|
|
\[ {}x y^{\prime \prime }+\frac {y^{\prime }}{2}+2 y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.381 |
|
|
\[ {}x^{2} y^{\prime \prime }-x y^{\prime }+y = 0 \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.588 |
|
|
\[ {}2 x y^{\prime \prime }-y^{\prime }+2 y = 0 \] |
kovacic, second_order_bessel_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.718 |
|
|
\[ {}x y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
kovacic |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.466 |
|
|
\[ {}x \left (-1+x \right )^{2} y^{\prime \prime }-2 y = 0 \] |
kovacic, second_order_bessel_ode |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.899 |
|
|
\[ {}y^{\prime }-\frac {2 y}{x}-x^{2} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.561 |
|
|
\[ {}y^{\prime }+\frac {2 y}{x}-x^{3} = 0 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.548 |
|
|
\[ {}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+m y = 0 \] |
unknown |
[_Laguerre] |
✗ |
N/A |
0.618 |
|
|
\[ {}x y^{\prime } = x^{2}+2 x -3 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.173 |
|
|
\[ {}\left (1+x \right )^{2} y^{\prime } = 1+y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.693 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{3 x} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.583 |
|
|
\[ {}-y+x y^{\prime } = x^{2} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.578 |
|
|
\[ {}x^{2} y^{\prime } = x^{3} \sin \left (3 x \right )+4 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.595 |
|
|
\[ {}x \cos \left (y\right ) y^{\prime }-\sin \left (y\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.332 |
|
|
\[ {}\left (x^{3}+x y^{2}\right ) y^{\prime } = 2 y^{3} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.816 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime }+2 x y = x \] |
exact, linear, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.437 |
|
|
\[ {}y^{\prime }+y \tanh \left (x \right ) = 2 \sinh \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.762 |
|
|
\[ {}x y^{\prime }-2 y = x^{3} \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.692 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = y^{3} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.257 |
|
|
\[ {}x y^{\prime }+3 y = x^{2} y^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.606 |
|
|
\[ {}x \left (y-3\right ) y^{\prime } = 4 y \] |
separable |
[_separable] |
✓ |
✓ |
0.481 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime } = x^{2} y \] |
separable |
[_separable] |
✓ |
✓ |
0.514 |
|
|
\[ {}x^{3}+\left (y+1\right )^{2} y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.513 |
|
|
\[ {}\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
1.862 |
|
|
\[ {}x^{2} \left (y+1\right )+y^{2} \left (-1+x \right ) y^{\prime } = 0 \] |
separable |
[_separable] |
✓ |
✓ |
0.279 |
|
|
\[ {}\left (2 y-x \right ) y^{\prime } = y+2 x \] |
homogeneous |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.664 |
|
|
\[ {}x y+y^{2}+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.401 |
|
|
\[ {}x^{3}+y^{3} = 3 x y^{2} y^{\prime } \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.616 |
|
|
\[ {}y-3 x +\left (4 y+3 x \right ) y^{\prime } = 0 \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.642 |
|
|
\[ {}\left (x^{3}+3 x y^{2}\right ) y^{\prime } = y^{3}+3 x^{2} y \] |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.565 |
|
|
\[ {}-y+x y^{\prime } = x^{3}+3 x^{2}-2 x \] |
linear |
[_linear] |
✓ |
✓ |
0.231 |
|
|
\[ {}y^{\prime }+y \tan \left (x \right ) = \sin \left (x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.239 |
|
|
\[ {}-y+x y^{\prime } = x^{3} \cos \left (x \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.531 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+3 x y = 5 x \] |
linear |
[_separable] |
✓ |
✓ |
0.491 |
|
|
|
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