Column notations: A is ODE degree. B is Program Number of solutions generated. C is CAS Number of solutions generated.
|
# |
ODE |
A |
B |
C |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime } = 2 x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.141 |
|
|
\[ {}x y^{\prime } = 2 y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.975 |
|
|
\[ {}y y^{\prime } = {\mathrm e}^{2 x} \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.77 |
|
|
\[ {}y^{\prime } = k y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.658 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.396 |
|
|
\[ {}y^{\prime \prime }-4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.219 |
|
|
\[ {}x y^{\prime }+y = y^{\prime } \sqrt {1-x^{2} y} \] |
1 |
0 |
0 |
unknown |
[_rational] |
❇ |
N/A |
16.67 |
|
|
\[ {}x y^{\prime } = y+x^{2}+y^{2} \] |
1 |
1 |
1 |
riccati, exactByInspection, homogeneousTypeD2 |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
1.287 |
|
|
\[ {}y^{\prime } = \frac {x y}{x^{2}+y^{2}} \] |
1 |
1 |
1 |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.279 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
1 |
1 |
2 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.457 |
|
|
\[ {}x y^{\prime }+y = x^{4} {y^{\prime }}^{2} \] |
2 |
2 |
5 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
7.297 |
|
|
\[ {}y^{\prime } = \frac {y^{2}}{x y-x^{2}} \] |
1 |
1 |
1 |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.466 |
|
|
\[ {}\left (y \cos \left (y\right )-\sin \left (y\right )+x \right ) y^{\prime } = y \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.437 |
|
|
\[ {}1+y^{2}+y^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.329 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3 x}-x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.183 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.168 |
|
|
\[ {}\left (1+x \right ) y^{\prime } = x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.198 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.191 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime } = \arctan \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.419 |
|
|
\[ {}x y^{\prime } = 1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.128 |
|
|
\[ {}y^{\prime } = \arcsin \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.172 |
|
|
\[ {}\sin \left (x \right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.266 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime } = x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.243 |
|
|
\[ {}\left (x^{2}-3 x +2\right ) y^{\prime } = x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.362 |
|
|
\[ {}y^{\prime } = x \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.275 |
|
|
\[ {}y^{\prime } = 2 \sin \left (x \right ) \cos \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.489 |
|
|
\[ {}y^{\prime } = \ln \left (x \right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.3 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.385 |
|
|
\[ {}x \left (x^{2}-4\right ) y^{\prime } = 1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.425 |
|
|
\[ {}\left (1+x \right ) \left (x^{2}+1\right ) y^{\prime } = 2 x^{2}+x \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime } = 2 x y+1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.773 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.26 |
|
|
\[ {}y^{\prime } = \frac {2 x y^{2}}{1-x^{2} y} \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.313 |
|
|
\[ {}2 y^{\prime \prime \prime }+y^{\prime \prime }-5 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.25 |
|
|
\[ {}x^{5} y^{\prime }+y^{5} = 0 \] |
1 |
1 |
4 |
separable |
[_separable] |
✓ |
✓ |
0.279 |
|
|
\[ {}y^{\prime } = 4 x y \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.278 |
|
|
\[ {}y^{\prime }+\tan \left (x \right ) y = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.499 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+1+y^{2} = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.289 |
|
|
\[ {}y \ln \left (y\right )-x y^{\prime } = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.781 |
|
|
\[ {}x y^{\prime } = \left (-4 x^{2}+1\right ) \tan \left (y\right ) \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.354 |
|
|
\[ {}y^{\prime } \sin \left (y\right ) = x^{2} \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.329 |
|
|
\[ {}y^{\prime }-\tan \left (x \right ) y = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.445 |
|
|
\[ {}x y y^{\prime } = y-1 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.381 |
|
|
\[ {}x y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.161 |
|
|
\[ {}y y^{\prime } = 1+x \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.855 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.589 |
|
|
\[ {}\frac {y^{\prime }}{x^{2}+1} = \frac {x}{y} \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.887 |
|
|
\[ {}y^{2} y^{\prime } = 2+x \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
1.717 |
|
|
\[ {}y^{\prime } = x^{2} y^{2} \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
0.424 |
|
|
\[ {}\left (y+1\right ) y^{\prime } = -x^{2}+1 \] |
1 |
1 |
1 |
separable |
[_separable] |
✓ |
✓ |
1.011 |
|
|
\[ {}\frac {y^{\prime \prime }}{y^{\prime }} = x^{2} \] |
1 |
1 |
1 |
second_order_integrable_as_is, second_order_ode_missing_y, exact nonlinear second order ode |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime \prime } y^{\prime } = \left (1+x \right ) x \] |
1 |
2 |
2 |
second_order_integrable_as_is, second_order_ode_missing_y, exact nonlinear second order ode |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
3.369 |
|
|
\[ {}y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
linear |
[_separable] |
✓ |
✓ |
0.277 |
|
|
\[ {}y^{\prime }+x y = x \] |
1 |
1 |
1 |
linear |
[_separable] |
✓ |
✓ |
0.284 |
|
|
\[ {}y^{\prime }+y = \frac {1}{{\mathrm e}^{2 x}+1} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.287 |
|
|
\[ {}y^{\prime }+y = 2 x \,{\mathrm e}^{-x}+x^{2} \] |
1 |
1 |
1 |
linear |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.249 |
|
|
\[ {}2 y-x^{3} = x y^{\prime } \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.21 |
|
|
\[ {}y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
linear |
[_separable] |
✓ |
✓ |
0.267 |
|
|
\[ {}x y^{\prime }-3 y = x^{4} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.2 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime }+2 x y = \cot \left (x \right ) \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.23 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = 2 x \csc \left (x \right ) \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.308 |
|
|
\[ {}y-x +x y \cot \left (x \right )+x y^{\prime } = 0 \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.405 |
|
|
\[ {}y^{\prime }-x y = 0 \] |
1 |
1 |
1 |
linear |
[_separable] |
✓ |
✓ |
0.468 |
|
|
\[ {}y^{\prime }-2 x y = 6 x \,{\mathrm e}^{x^{2}} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.582 |
|
|
\[ {}x \ln \left (x \right ) y^{\prime }+y = 3 x^{3} \] |
1 |
0 |
0 |
linear |
[_linear] |
❇ |
N/A |
0.852 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
linear |
[_linear] |
✓ |
✓ |
0.53 |
|
|
\[ {}y^{\prime }+4 y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
linear |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.481 |
|
|
\[ {}x^{2} y^{\prime }+x y = 2 x \] |
1 |
1 |
1 |
linear |
[_separable] |
✓ |
✓ |
0.595 |
|
|
\[ {}x y^{\prime }+y = x^{4} y^{3} \] |
1 |
1 |
2 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.231 |
|
|
\[ {}x y^{2} y^{\prime }+y^{3} = x \cos \left (x \right ) \] |
1 |
1 |
3 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
8.563 |
|
|
\[ {}x y^{\prime }+y = x y^{2} \] |
1 |
1 |
1 |
riccati, bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.415 |
|
|
\[ {}y^{\prime }+x y = y^{4} x \] |
1 |
1 |
3 |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
7.695 |
|
|
\[ {}\left ({\mathrm e}^{y}-2 x y\right ) y^{\prime } = y^{2} \] |
1 |
1 |
1 |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.072 |
|
|
\[ {}y-x y^{\prime } = y^{\prime } y^{2} {\mathrm e}^{y} \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
1.62 |
|
|
\[ {}x y^{\prime }+2 = x^{3} \left (y-1\right ) y^{\prime } \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
5.012 |
|
|
\[ {}x y^{\prime } = 2 x^{2} y+y \ln \left (x \right ) \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.501 |
|
|
\[ {}y^{\prime } \sin \left (2 x \right ) = 2 y+2 \cos \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.145 |
|
|
\[ {}\left (x +\frac {2}{y}\right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.368 |
|
|
\[ {}\sin \left (x \right ) \tan \left (y\right )+1+\cos \left (x \right ) \sec \left (x \right )^{2} y y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[‘x=_G(y,y’)‘] |
❇ |
N/A |
45.073 |
|
|
\[ {}y-x^{3}+\left (x +y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
2.069 |
|
|
\[ {}2 y^{2}-4 x +5 = \left (4-2 y+4 x y\right ) y^{\prime } \] |
1 |
0 |
0 |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.807 |
|
|
\[ {}y+y \cos \left (x y\right )+\left (x +x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.158 |
|
|
\[ {}\cos \left (x \right ) \cos \left (y\right )^{2}+2 \sin \left (x \right ) \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
8.104 |
|
|
\[ {}\left (\sin \left (x \right ) \sin \left (y\right )-x \,{\mathrm e}^{y}\right ) y^{\prime } = {\mathrm e}^{y}+\cos \left (x \right ) \cos \left (y\right ) \] |
1 |
1 |
1 |
exact |
[_exact] |
✓ |
✓ |
15.332 |
|
|
\[ {}-\frac {\sin \left (\frac {x}{y}\right )}{y}+\frac {x \sin \left (\frac {x}{y}\right ) y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
exact |
[_separable] |
✓ |
✓ |
0.669 |
|
|
\[ {}1+y+\left (1-x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.761 |
|
|
\[ {}2 x y^{3}+y \cos \left (x \right )+\left (3 x^{2} y^{2}+\sin \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
54.746 |
|
|
\[ {}\frac {y}{1-x^{2} y^{2}}+\frac {x y^{\prime }}{1-x^{2} y^{2}} = 1 \] |
1 |
1 |
1 |
exact, riccati |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.265 |
|
|
\[ {}2 y^{4} x +\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact] |
✓ |
✓ |
4.274 |
|
|
\[ {}\frac {x y^{\prime }+y}{1-x^{2} y^{2}}+x = 0 \] |
1 |
1 |
1 |
exact, riccati |
[_exact, _rational, _Riccati] |
✓ |
✓ |
2.368 |
|
|
\[ {}2 x \left (1+\sqrt {x^{2}-y}\right ) = \sqrt {x^{2}-y}\, y^{\prime } \] |
1 |
1 |
1 |
exact, first_order_ode_lie_symmetry_calculated |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
7.158 |
|
|
\[ {}x \ln \left (y\right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.919 |
|
|
\[ {}{\mathrm e}^{y^{2}}-\csc \left (y\right ) \csc \left (x \right )^{2}+\left (2 x y \,{\mathrm e}^{y^{2}}-\csc \left (y\right ) \cot \left (y\right ) \cot \left (x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact] |
✓ |
✓ |
84.118 |
|
|
\[ {}1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[_exact, _Bernoulli] |
✓ |
✓ |
0.707 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
exact |
[_separable] |
✓ |
✓ |
0.289 |
|
|
\[ {}3 x^{2} \left (1+\ln \left (y\right )\right )+\left (\frac {x^{3}}{y}-2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.157 |
|
|
\[ {}\frac {y-x y^{\prime }}{\left (x +y\right )^{2}}+y^{\prime } = 1 \] |
1 |
1 |
2 |
exact, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
8.179 |
|
|
\[ {}\frac {4 y^{2}-2 x^{2}}{4 x y^{2}-x^{3}}+\frac {\left (8 y^{2}-x^{2}\right ) y^{\prime }}{4 y^{3}-x^{2} y} = 0 \] |
1 |
1 |
4 |
exact |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
8.88 |
|
|
\[ {}x^{2}-2 y^{2}+x y y^{\prime } = 0 \] |
1 |
1 |
2 |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.757 |
|
|
\[ {}x^{2} y^{\prime }-3 x y-2 y^{2} = 0 \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.941 |
|
|
\[ {}x^{2} y^{\prime } = 3 \left (x^{2}+y^{2}\right ) \arctan \left (\frac {y}{x}\right )+x y \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.297 |
|
|
\[ {}x \sin \left (\frac {y}{x}\right ) y^{\prime } = y \sin \left (\frac {y}{x}\right )+x \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.29 |
|
|
\[ {}x y^{\prime } = y+2 x \,{\mathrm e}^{-\frac {y}{x}} \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.743 |
|
|
\[ {}x -y-\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
homogeneous |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.356 |
|
|
\[ {}x y^{\prime } = 2 x -6 y \] |
1 |
1 |
1 |
homogeneous |
[_linear] |
✓ |
✓ |
1.391 |
|
|
\[ {}x y^{\prime } = \sqrt {x^{2}+y^{2}} \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
1.622 |
|
|
\[ {}x^{2} y^{\prime } = y^{2}+2 x y \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.885 |
|
|
\[ {}x^{3}+y^{3}-x y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
homogeneous |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.695 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x -y-6} \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.154 |
|
|
\[ {}y^{\prime } = \frac {x +y+4}{x +y-6} \] |
1 |
1 |
1 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.968 |
|
|
\[ {}2 x -2 y+\left (y-1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.46 |
|
|
\[ {}y^{\prime } = \frac {x +y-1}{x +4 y+2} \] |
1 |
1 |
1 |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
11.516 |
|
|
\[ {}2 x +3 y-1-4 \left (1+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.355 |
|
|
\[ {}y^{\prime } = \frac {1-x y^{2}}{2 x^{2} y} \] |
1 |
1 |
2 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = \frac {2+3 x y^{2}}{4 x^{2} y} \] |
1 |
1 |
2 |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.215 |
|
|
\[ {}y^{\prime } = \frac {y-x y^{2}}{x +x^{2} y} \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.674 |
|
|
\[ {}y^{\prime } = \sin \left (\frac {y}{x}\right )-\cos \left (\frac {y}{x}\right ) \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.257 |
|
|
\[ {}{\mathrm e}^{\frac {x}{y}}-\frac {y y^{\prime }}{x} = 0 \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.097 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-x y}{y^{2} \cos \left (\frac {x}{y}\right )} \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
4.489 |
|
|
\[ {}y^{\prime } = \frac {y \tan \left (\frac {y}{x}\right )}{x} \] |
1 |
1 |
1 |
homogeneous |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.023 |
|
|
\[ {}\left (3 x^{2}-y^{2}\right ) y^{\prime }-2 x y = 0 \] |
1 |
1 |
3 |
exact |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
0.444 |
|
|
\[ {}x y-1+\left (x^{2}-x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.382 |
|
|
\[ {}x y^{\prime }+y+3 x^{3} y^{4} y^{\prime } = 0 \] |
1 |
1 |
4 |
exact |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.537 |
|
|
\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 y \csc \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.559 |
|
|
\[ {}\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_separable] |
✓ |
✓ |
1.457 |
|
|
\[ {}y+\left (x -2 x^{2} y^{3}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
0.472 |
|
|
\[ {}x +3 y^{2}+2 x y y^{\prime } = 0 \] |
1 |
1 |
2 |
exact |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.338 |
|
|
\[ {}y+\left (2 x -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
0.443 |
|
|
\[ {}y \ln \left (y\right )-2 x y+\left (x +y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
0.879 |
|
|
\[ {}y^{2}+x y+1+\left (x^{2}+x y+1\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.46 |
|
|
\[ {}x^{3}+x y^{3}+3 y^{2} y^{\prime } = 0 \] |
1 |
1 |
3 |
exact |
[_rational, _Bernoulli] |
✓ |
✓ |
0.455 |
|
|
\[ {}y^{\prime } = \frac {2 y}{x}+\frac {x^{3}}{y}+x \tan \left (\frac {y}{x^{2}}\right ) \] |
1 |
1 |
2 |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
24.117 |
|
|
\[ {}y y^{\prime \prime }+{y^{\prime }}^{2} = 0 \] |
1 |
2 |
3 |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
2.132 |
|
|
\[ {}x y y^{\prime \prime } = y^{\prime }+{y^{\prime }}^{3} \] |
1 |
0 |
0 |
unknown |
[NONE] |
❇ |
N/A |
0.144 |
|
|
\[ {}y^{\prime \prime }-k^{2} y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.232 |
|
|
\[ {}x^{2} y^{\prime \prime } = 2 x y^{\prime }+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
1.188 |
|
|
\[ {}2 y y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.38 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.647 |
|
|
\[ {}x y^{\prime \prime }+y^{\prime } = 4 x \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
2.368 |
|
|
\[ {}\left (x^{2}+2 y^{\prime }\right ) y^{\prime \prime }+2 x y^{\prime } = 0 \] |
1 |
2 |
2 |
second_order_integrable_as_is, second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
65.544 |
|
|
\[ {}y y^{\prime \prime } = y^{2} y^{\prime }+{y^{\prime }}^{2} \] |
1 |
1 |
1 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
5.231 |
|
|
\[ {}y^{\prime \prime } = {\mathrm e}^{y} y^{\prime } \] |
1 |
1 |
1 |
second_order_integrable_as_is, second_order_ode_missing_x, exact nonlinear second order ode |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
4.645 |
|
|
\[ {}y^{\prime \prime } = 1+{y^{\prime }}^{2} \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.93 |
|
|
\[ {}y^{\prime \prime }+{y^{\prime }}^{2} = 1 \] |
1 |
2 |
1 |
second_order_ode_missing_x, second_order_ode_missing_y |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
9.789 |
|
|
\[ {}x y^{\prime }+y = x \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.171 |
|
|
\[ {}x^{2} y^{\prime }+y = x^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.694 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.053 |
|
|
\[ {}\sec \left (x \right ) y^{\prime } = \sec \left (y\right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.589 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+y^{2}}{x^{2}-y^{2}} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.42 |
|
|
\[ {}y^{\prime } = \frac {2 y+x}{2 x -y} \] |
1 |
1 |
1 |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.238 |
|
|
\[ {}2 x y+x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.572 |
|
|
\[ {}-\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
41.194 |
|
|
\[ {}-y+x y^{\prime } = 2 x \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.21 |
|
|
\[ {}x^{2} y^{\prime }-2 y = 3 x^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
23.692 |
|
|
\[ {}y^{2} y^{\prime } = x \] |
1 |
1 |
1 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
163.036 |
|
|
\[ {}\csc \left (x \right ) y^{\prime } = \csc \left (y\right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.879 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.302 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+2 y^{2}}{x^{2}-2 y^{2}} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
2.646 |
|
|
\[ {}2 x \cos \left (y\right )-x^{2} \sin \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
17.418 |
|
|
\[ {}\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} = 0 \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.627 |
|
|
\[ {}y y^{\prime \prime }-{y^{\prime }}^{2} = 0 \] |
1 |
1 |
2 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
3.014 |
|
|
\[ {}x y^{\prime \prime } = y^{\prime }-2 {y^{\prime }}^{3} \] |
1 |
2 |
2 |
second_order_ode_missing_y |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
15.584 |
|
|
\[ {}y y^{\prime \prime }+y^{\prime } = 0 \] |
1 |
1 |
2 |
second_order_ode_missing_x |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
1.801 |
|
|
\[ {}x y^{\prime \prime }-3 y^{\prime } = 5 x \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
6.202 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.399 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.507 |
|
|
\[ {}y^{\prime \prime }+8 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.45 |
|
|
\[ {}2 y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.735 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.507 |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+20 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.418 |
|
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.419 |
|
|
\[ {}4 y^{\prime \prime }-12 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.543 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.593 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.192 |
|
|
\[ {}4 y^{\prime \prime }+20 y^{\prime }+25 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.55 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.168 |
|
|
\[ {}y^{\prime \prime } = 4 y \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.666 |
|
|
\[ {}4 y^{\prime \prime }-8 y^{\prime }+7 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.282 |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.425 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.649 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.579 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }-5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.42 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.832 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.096 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.019 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.768 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.98 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
3.615 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+10 x y^{\prime }+8 y = 0 \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
3.474 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y = 0 \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
2.625 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_euler_ode |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.76 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
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)]‘]] |
✓ |
✓ |
3.393 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
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], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.582 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
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]] |
✓ |
✓ |
3.976 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
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)]‘]] |
✓ |
✓ |
3.53 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-16 y = 0 \] |
1 |
1 |
1 |
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)]‘]] |
✓ |
✓ |
3.069 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-10 y = 6 \,{\mathrm e}^{4 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.782 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.191 |
|
|
\[ {}y^{\prime \prime }+10 y^{\prime }+25 y = 14 \,{\mathrm e}^{-5 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.946 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 25 x^{2}+12 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.792 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = 20 \,{\mathrm e}^{-2 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.808 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = 14 \sin \left (2 x \right )-18 \cos \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.423 |
|
|
\[ {}y^{\prime \prime }+y = 2 \cos \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.309 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = 12 x -10 \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
5.402 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 6 \,{\mathrm e}^{x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.877 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = {\mathrm e}^{x} \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.22 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = 10 x^{4}+2 \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
3.957 |
|
|
\[ {}y^{\prime \prime }+4 y = 4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.109 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \sin \left (3 x \right )+4 \sin \left (x \right )-26 \,{\mathrm e}^{-2 x}+27 x^{3} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
9.024 |
|
|
\[ {}y^{\prime \prime }-3 y = {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.917 |
|
|
\[ {}y^{\prime \prime \prime }+y^{\prime } = \sin \left (x \right ) \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
2.069 |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.411 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-x} \ln \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.049 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-3 y = 64 x \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.817 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{-x} \sec \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.585 |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }+y = {\mathrm e}^{-3 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.76 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = \frac {1}{1+{\mathrm e}^{-x}} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.865 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.905 |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (x \right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.451 |
|
|
\[ {}y^{\prime \prime }+y = \cot \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.959 |
|
|
\[ {}y^{\prime \prime }+y = x \cos \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.374 |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.922 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \tan \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.986 |
|
|
\[ {}y^{\prime \prime }+y = \sec \left (x \right ) \csc \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.848 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 2 x \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.872 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.718 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = \left (x^{2}-1\right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.388 |
|
|
\[ {}\left (x^{2}+x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-\left (2+x \right ) y = x \left (1+x \right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.458 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = \left (1-x \right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_change_of_variable_on_y_method_2, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.786 |
|
|
\[ {}x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+y = x^{2} {\mathrm e}^{2 x} \] |
1 |
1 |
1 |
kovacic, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.931 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = x \,{\mathrm e}^{-x} \] |
1 |
1 |
1 |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.461 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.414 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.345 |
|
|
\[ {}x y^{\prime \prime }+3 y^{\prime } = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
0.642 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.668 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[_Gegenbauer] |
✓ |
✓ |
1.02 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime \prime }-\frac {x y^{\prime }}{-1+x}+\frac {y}{-1+x} = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.122 |
|
|
\[ {}x^{2} y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.676 |
|
|
\[ {}x^{2} y^{\prime \prime }-x \left (2+x \right ) y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.072 |
|
|
\[ {}y^{\prime \prime }-x f \left (x \right ) y^{\prime }+f \left (x \right ) y = 0 \] |
1 |
1 |
1 |
second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.041 |
|
|
\[ {}x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.328 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.375 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.618 |
|
|
\[ {}y^{\prime \prime \prime }-y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
1.204 |
|
|
\[ {}y^{\prime \prime \prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
1.218 |
|
|
\[ {}y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.199 |
|
|
\[ {}y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+6 y^{\prime \prime }+4 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.214 |
|
|
\[ {}y^{\prime \prime \prime \prime }-y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.549 |
|
|
\[ {}y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.889 |
|
|
\[ {}y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.212 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 a^{2} y^{\prime \prime }+a^{4} y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.233 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+2 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.752 |
|
|
\[ {}y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.875 |
|
|
\[ {}y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
0.418 |
|
|
\[ {}y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }-5 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.235 |
|
|
\[ {}y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+48 y^{\prime \prime }+16 y^{\prime }-96 y = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _missing_x]] |
✓ |
✓ |
0.708 |
|
|
\[ {}y^{\prime \prime \prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.305 |
|
|
\[ {}y^{\prime \prime \prime \prime } = \sin \left (x \right )+24 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_high_order, _quadrature]] |
✓ |
✓ |
0.392 |
|
|
\[ {}y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime } = 10+42 \,{\mathrm e}^{3 x} \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
1.159 |
|
|
\[ {}y^{\prime \prime \prime }-y^{\prime } = 1 \] |
1 |
1 |
1 |
higher_order_linear_constant_coefficients_ODE |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
1.319 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime } = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
0.753 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.801 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
1 |
1 |
higher_order_ODE_non_constant_coefficients_of_type_Euler |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.995 |
|
|
\[ {}x^{3} y^{\prime \prime \prime \prime }+8 x^{2} y^{\prime \prime \prime }+8 x y^{\prime \prime }-8 y^{\prime } = 0 \] |
1 |
1 |
1 |
higher_order_missing_y |
[[_high_order, _missing_y]] |
✓ |
✓ |
1.242 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.846 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.528 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.313 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-5 y = x \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.996 |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.924 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.971 |
|
|
\[ {}y^{\prime \prime }-y = {\mathrm e}^{3 x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime \prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
14.71 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+4 y = x \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.164 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = {\mathrm e}^{x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.602 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+4 y = \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
10.681 |
|
|
\[ {}y^{\prime \prime }+y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.026 |
|
|
\[ {}y^{\prime \prime }-y = \cos \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.87 |
|
|
\[ {}y^{\prime \prime } = \tan \left (x \right ) \] |
1 |
1 |
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 |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
20.485 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime } = \ln \left (x \right ) \] |
1 |
1 |
1 |
kovacic, exact linear second order ode, second_order_integrable_as_is, second_order_ode_missing_y, second_order_linear_constant_coeff |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
9.974 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 x -1 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.724 |
|
|
\[ {}y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{-x} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = \cos \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.863 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = x \,{\mathrm e}^{x} \sin \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.601 |
|
|
\[ {}y^{\prime \prime }+9 y = \sec \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.189 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = x \ln \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.442 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+y = \frac {2}{x} \] |
1 |
1 |
1 |
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 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
7.598 |
|
|
\[ {}y^{\prime \prime }+4 y = \tan \left (x \right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.031 |
|
|
\[ {}y^{\prime \prime }-y = 3 \,{\mathrm e}^{2 x} \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.342 |
|
|
\[ {}y^{\prime \prime }+y = -8 \sin \left (3 x \right ) \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.286 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{2}+2 x +2 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.068 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } = \frac {-1+x}{x} \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
26.779 |
|
|
\[ {}x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
6.595 |
|
|
\[ {}y^{\prime \prime }+9 y = -3 \cos \left (2 x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.618 |
|
|
\[ {}y^{\prime }+y = \cos \left (x \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.008 |
|
|
\[ {}y^{\prime \prime } = -3 y \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
13.961 |
|
|
\[ {}y^{\prime \prime }+\sin \left (y\right ) = 0 \] |
1 |
2 |
2 |
second_order_ode_missing_x, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
7.572 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
1.259 |
|
|
\[ {}y^{\prime } = 2 x y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.815 |
|
|
\[ {}y^{\prime }+y = 1 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.225 |
|
|
\[ {}y^{\prime }+y = 1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.392 |
|
|
\[ {}y^{\prime }-y = 2 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.184 |
|
|
\[ {}y^{\prime }-y = 2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime }+y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime }+y = 0 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.235 |
|
|
\[ {}y^{\prime }-y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.718 |
|
|
\[ {}y^{\prime }-y = 0 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.205 |
|
|
\[ {}y^{\prime }-y = x^{2} \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime }-y = x^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.397 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
first order ode series method. Regular singular point |
[_separable] |
✓ |
✓ |
0.7 |
|
|
\[ {}x y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.5 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
0 |
0 |
first order ode series method. Irregular singular point |
[_separable] |
❇ |
N/A |
0.833 |
|
|
\[ {}x^{2} y^{\prime } = y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.664 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
first order ode series method. Regular singular point |
[_linear] |
✓ |
✓ |
0.982 |
|
|
\[ {}y^{\prime }-\frac {y}{x} = x^{2} \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.743 |
|
|
\[ {}y^{\prime }+\frac {y}{x} = x \] |
1 |
1 |
1 |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.173 |
|
|
\[ {}y^{\prime } = \frac {1}{\sqrt {-x^{2}+1}} \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
1.063 |
|
|
\[ {}y^{\prime } = y+1 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.765 |
|
|
\[ {}y^{\prime } = x -y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[[_linear, ‘class A‘]] |
✓ |
✓ |
7.867 |
|
|
\[ {}y^{\prime } = x -y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.708 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.6 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}y^{\prime \prime }+2 x y^{\prime }-y = x \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.941 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x^{2} y = 1 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.894 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
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)]‘]] |
✓ |
✓ |
1.693 |
|
|
\[ {}y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.433 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.546 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.254 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.583 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.191 |
|
|
\[ {}y^{\prime \prime }+\left (p +\frac {1}{2}-\frac {x^{2}}{4}\right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.589 |
|
|
\[ {}y^{\prime \prime }+x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.131 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.573 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+2 p y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.516 |
|
|
\[ {}x^{3} \left (-1+x \right ) y^{\prime \prime }-2 \left (-1+x \right ) y^{\prime }+3 x y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
6.504 |
|
|
\[ {}x^{2} \left (x^{2}-1\right ) y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
10.205 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (2-x \right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _missing_y]] |
❇ |
N/A |
0.425 |
|
|
\[ {}\left (1+3 x \right ) x y^{\prime \prime }-\left (1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.423 |
|
|
\[ {}y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
9.463 |
|
|
\[ {}x y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
6.506 |
|
|
\[ {}x^{2} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.851 |
|
|
\[ {}x^{3} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.432 |
|
|
\[ {}x^{4} y^{\prime \prime }+\sin \left (x \right ) y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
2.889 |
|
|
\[ {}x^{3} y^{\prime \prime }+\left (-1+\cos \left (2 x \right )\right ) y^{\prime }+2 x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
39.095 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+\left (2 x^{4}-5 x \right ) y^{\prime }+\left (3 x^{2}+2\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.792 |
|
|
\[ {}x^{2} y^{\prime \prime }+3 x y^{\prime }+4 x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
7.579 |
|
|
\[ {}x^{3} y^{\prime \prime }-4 x^{2} y^{\prime }+3 x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.538 |
|
|
\[ {}4 x y^{\prime \prime }+3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.832 |
|
|
\[ {}2 x y^{\prime \prime }+\left (-x +3\right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.984 |
|
|
\[ {}2 x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.271 |
|
|
\[ {}2 x^{2} y^{\prime \prime }+x y^{\prime }-\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.92 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+x^{2} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
2.013 |
|
|
\[ {}y^{\prime \prime }+\frac {y^{\prime }}{x^{2}}-\frac {y}{x^{3}} = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
❇ |
N/A |
0.641 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0 \] |
1 |
0 |
0 |
second order series method. Irregular singular point |
[[_2nd_order, _exact, _linear, _homogeneous]] |
❇ |
N/A |
0.927 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (4 x +4\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.501 |
|
|
\[ {}4 x^{2} y^{\prime \prime }-8 x^{2} y^{\prime }+\left (4 x^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.294 |
|
|
\[ {}x y^{\prime \prime }+2 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.411 |
|
|
\[ {}x^{2} y^{\prime \prime }-x^{2} y^{\prime }+\left (x^{2}-2\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.453 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.519 |
|
|
\[ {}\left (-1+x \right )^{2} y^{\prime \prime }-3 \left (-1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.141 |
|
|
\[ {}3 \left (1+x \right )^{2} y^{\prime \prime }-\left (1+x \right ) y^{\prime }-y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.967 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
6.876 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.597 |
|
|
\[ {}x \left (1-x \right ) y^{\prime \prime }+\left (\frac {3}{2}-2 x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[_Jacobi] |
✓ |
✓ |
3.153 |
|
|
\[ {}\left (2 x^{2}+2 x \right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.782 |
|
|
\[ {}\left (x^{2}-1\right ) y^{\prime \prime }+\left (5 x +4\right ) y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.117 |
|
|
\[ {}\left (x^{2}-x -6\right ) y^{\prime \prime }+\left (5+3 x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
24.812 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+p^{2} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
4.711 |
|
|
\[ {}\left (-{\mathrm e}^{x}+1\right ) y^{\prime \prime }+\frac {y^{\prime }}{2}+{\mathrm e}^{x} y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
4.176 |
|
|
\[ {}y^{\prime \prime }+2 x y = x^{2} \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.428 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }+y = x \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.408 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+y = x^{3}-x \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.9 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
1.777 |
|
|
\[ {}\left (x^{2}+4\right ) y^{\prime \prime }-y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.219 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.671 |
|
|
\[ {}y^{\prime \prime }-\left (1+x \right ) y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.997 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.751 |
|
|
\[ {}\left (x^{2}+1\right ) x^{2} y^{\prime \prime }-x y^{\prime }+\left (2+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
16.607 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (1+x \right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.891 |
|
|
\[ {}x y^{\prime \prime }-4 y^{\prime }+x y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
3.286 |
|
|
\[ {}4 x^{2} y^{\prime \prime }+4 x^{2} y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
7.754 |
|
|
\[ {}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.217 |
|
|
\[ {}x y^{\prime \prime }-\left (-1+x \right ) y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[_Laguerre] |
✓ |
✓ |
3.061 |
|
|
\[ {}x^{2} y^{\prime \prime }+x \left (1-x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
8.414 |
|
|
\[ {}x y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.652 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+x y = 0 \] |
1 |
0 |
1 |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-3 x y^{\prime }+\left (-1+x \right ) y = 0 \] |
1 |
0 |
1 |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+\left (x^{2}+2 x \right ) y^{\prime }-x y = 0 \] |
1 |
0 |
1 |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime \prime }+\left (2 x^{3}-x^{2}\right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
0 |
1 |
unknown |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
N/A |
0.0 |
|
|
\[ {}x^{3} y^{\prime \prime }+x^{2} y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.698 |
|
|
\[ {}9 \left (-2+x \right )^{2} \left (x -3\right ) y^{\prime \prime }+6 x \left (-2+x \right ) y^{\prime }+16 y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
24.606 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+p \left (p +1\right ) y = 0 \] |
1 |
1 |
1 |
second order series method. Regular singular point. Difference not integer |
[_Gegenbauer] |
✓ |
✓ |
5.185 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 5 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.156 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = t \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.085 |
|
|
\[ {}y^{\prime \prime }-y = t^{2} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.032 |
|
|
\[ {}L i^{\prime }+R i = E_{0} \operatorname {Heaviside}\left (t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.074 |
|
|
\[ {}L i^{\prime }+R i = E_{0} \delta \left (t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
3.217 |
|
|
|
|||||||||
|
\[ {}L i^{\prime }+R i = E_{0} \sin \left (\omega t \right ) \] |
1 |
1 |
1 |
first_order_laplace |
[[_linear, ‘class A‘]] |
✓ |
✓ |
2.338 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-5 y = 1 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.069 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }-2 y = -6 \,{\mathrm e}^{\pi -t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.226 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-y = t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.172 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.142 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.611 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+3 y = 2 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+2 y = t \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.145 |
|
|
\[ {}y^{\prime \prime }-7 y^{\prime }+12 y = t \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.486 |
|
|
\[
{}i^{\prime \prime }+2 i^{\prime }+3 i = \left \{\begin {array}{cc} 30 & 0 |
1 |
1 |
0 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
31.611 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.528 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+3 y \\ y^{\prime }=3 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.533 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=3 x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.507 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y+t -1 \\ y^{\prime }=3 x+2 y-5 t -2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.434 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.276 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.316 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+4 y \\ y^{\prime }=-2 x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.445 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=5 x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.783 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=-x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-3 y \\ y^{\prime }=8 x-6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.502 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.315 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-y \\ y^{\prime }=x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.53 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=7 x+6 y \\ y^{\prime }=2 x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.512 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-2 y \\ y^{\prime }=4 x+5 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.746 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y-5 t +2 \\ y^{\prime }=4 x-2 y-8 t -8 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.213 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-4 y \\ y^{\prime }=4 x-7 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.511 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=4 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.52 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+\sqrt {2}\, y \\ y^{\prime }=\sqrt {2}\, x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.451 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+3 y \\ y^{\prime }=-6 x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.542 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.47 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x-5 y \\ y^{\prime }=-x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y \\ y^{\prime }=-4 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.826 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+2 y+z \\ y^{\prime }=-2 x-y+3 z \\ z^{\prime }=x+y+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.849 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+y-z \\ y^{\prime }=2 x-y-4 z \\ z^{\prime }=3 x-y+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
19.142 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+2 y-4 t +1 \\ y^{\prime }=-x+2 y+3 t +4 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.825 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y-t +3 \\ y^{\prime }=x+4 y+t -2 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.8 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y-t +3 \\ y^{\prime }=-x-5 y+t +1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.335 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x y+1 \\ y^{\prime }=-x+y \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.273 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=t y+1 \\ y^{\prime }=-x t +y \end {array}\right ] \] |
1 |
0 |
0 |
system of linear ODEs |
system of linear ODEs |
❇ |
N/A |
0.026 |
|
|
|
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