|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\sin \left (y \right )^{2} = x^{\prime } \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime } = \frac {\sqrt {t}}{y} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.73 |
|
|
\[ {}y^{\prime } = \sqrt {\frac {y}{t}} \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
123.202 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t}}{y+1} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.654 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{t -y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = \frac {y}{\ln \left (y\right )} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.535 |
|
|
\[ {}y^{\prime } = t \sin \left (t^{2}\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.757 |
|
|
\[ {}y^{\prime } = \frac {1}{x^{2}+1} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.374 |
|
|
\[ {}y^{\prime } = \frac {\sin \left (x \right )}{\cos \left (y\right )+1} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.88 |
|
|
\[ {}y^{\prime } = \frac {3+y}{1+3 x} \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.444 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x -y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.232 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x -y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.476 |
|
|
\[ {}y^{\prime } = \frac {3 y+1}{x +3} \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.701 |
|
|
\[ {}y^{\prime } = y \cos \left (t \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime } = y^{2} \cos \left (t \right ) \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.333 |
|
|
\[ {}y^{\prime } = \sqrt {y}\, \cos \left (t \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.479 |
|
|
\[ {}y^{\prime }+y f \left (t \right ) = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.801 |
|
|
\[ {}y^{\prime } = -\frac {y-2}{-2+x} \] |
exact, linear, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.186 |
|
|
\[ {}y^{\prime } = \frac {x +y+3}{3 x +3 y+1} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.496 |
|
|
\[ {}y^{\prime } = \frac {x -y+2}{2 x -2 y-1} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.58 |
|
|
\[ {}y^{\prime } = \left (x +y-4\right )^{2} \] |
riccati, homogeneousTypeC, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
1.074 |
|
|
\[ {}y^{\prime } = \left (3 y+1\right )^{4} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.407 |
|
|
\[ {}y^{\prime } = 3 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.467 |
|
|
\[ {}y^{\prime } = -y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.468 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.835 |
|
|
\[ {}y^{\prime } = 16 y-8 y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime } = 12+4 y-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.947 |
|
|
\[ {}y^{\prime } = y f \left (t \right ) \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.638 |
|
|
\[ {}y^{\prime }-y = 10 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.375 |
|
|
\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.894 |
|
|
\[ {}y^{\prime }-y = 2 \cos \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.11 |
|
|
\[ {}y^{\prime }-y = t^{2}-2 t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime }-y = 4 t \,{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}t y^{\prime }+y = t^{2} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.039 |
|
|
\[ {}t y^{\prime }+y = t \] |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.537 |
|
|
\[ {}x y^{\prime }+y = x \,{\mathrm e}^{x} \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.965 |
|
|
\[ {}x y^{\prime }+y = {\mathrm e}^{-x} \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.992 |
|
|
\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 2 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.048 |
|
|
\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}+1} = 4 t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.078 |
|
|
\[ {}y^{\prime } = 2 x +\frac {x y}{x^{2}-1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime }+y \cot \left (t \right ) = \cos \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.421 |
|
|
\[ {}y^{\prime }-\frac {3 t y}{t^{2}-4} = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.097 |
|
|
\[ {}y^{\prime }-\frac {4 t y}{4 t^{2}-9} = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime }-\frac {9 x y}{9 x^{2}+49} = x \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.084 |
|
|
\[ {}y^{\prime }+2 y \cot \left (x \right ) = \cos \left (x \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.288 |
|
|
\[ {}y^{\prime }+x y = x^{3} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.894 |
|
|
\[ {}y^{\prime }-x y = x \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.14 |
|
|
\[ {}y^{\prime } = \frac {1}{x +y^{2}} \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
0.976 |
|
|
\[ {}y^{\prime }-x = y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.776 |
|
|
\[ {}y-\left (x +3 y^{2}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
1.014 |
|
|
\[ {}x^{\prime } = \frac {3 x t^{2}}{-t^{3}+1} \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.479 |
|
|
\[ {}p^{\prime } = t^{3}+\frac {p}{t} \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.995 |
|
|
\[ {}v^{\prime }+v = {\mathrm e}^{-s} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime }-y = 4 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.116 |
|
|
\[ {}y^{\prime }+3 t^{2} y = {\mathrm e}^{-t^{3}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.23 |
|
|
\[ {}y^{\prime }+2 t y = 2 t \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.138 |
|
|
\[ {}t y^{\prime }+y = \cos \left (t \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.395 |
|
|
\[ {}t y^{\prime }+y = 2 \,{\mathrm e}^{t} t \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.293 |
|
|
\[ {}\left (1+{\mathrm e}^{t}\right ) y^{\prime }+y \,{\mathrm e}^{t} = t \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.49 |
|
|
\[ {}\left (t^{2}+4\right ) y^{\prime }+2 t y = 2 t \] |
exact, linear, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.252 |
|
|
\[ {}x^{\prime } = x+t +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.076 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 t}+2 y \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.102 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \ln \left (t \right ) \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.043 |
|
|
\[ {}y^{\prime \prime }-\frac {y^{\prime }}{t}+\frac {y}{t^{2}} = \frac {1}{t} \] |
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 |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.964 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} 4 & 0\le t <2 \\ 0 & 2\le t \end {array}\right . \] |
linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
4.965 |
|
|
\[ {}y^{\prime }+y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 0 & 1\le t \end {array}\right . \] |
linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
4.58 |
|
|
\[ {}y^{\prime }-y = \sin \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime }+y = 5 \,{\mathrm e}^{2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.919 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.858 |
|
|
\[ {}y^{\prime }+y = 2-{\mathrm e}^{2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.918 |
|
|
\[ {}y^{\prime }-5 y = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.876 |
|
|
\[ {}y^{\prime }+3 y = 27 t^{2}+9 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.898 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = 5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime }+4 y = 8 \cos \left (4 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.347 |
|
|
\[ {}y^{\prime }+10 y = 2 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime }-3 y = 27 t^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime }-y = 2 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime }+y = 4+3 \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.959 |
|
|
\[ {}y^{\prime }+y = 2 \cos \left (t \right )+t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.183 |
|
|
\[ {}y^{\prime }+\frac {y}{2} = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.462 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.385 |
|
|
\[ {}t y^{\prime }+y = t \cos \left (t \right ) \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.155 |
|
|
\[ {}y^{\prime }+y = t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.079 |
|
|
\[ {}y^{\prime }+y = \sin \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.336 |
|
|
\[ {}y^{\prime }+y = \cos \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.329 |
|
|
\[ {}y^{\prime }+y = {\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.079 |
|
|
\[ {}y^{2}-\frac {y}{2 \sqrt {t}}+\left (2 t y-\sqrt {t}+1\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
13.151 |
|
|
\[ {}\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}} = 0 \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.712 |
|
|
\[ {}y \cos \left (t y\right )+t \cos \left (t y\right ) y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y \sec \left (t \right )^{2}+2 t +\tan \left (t \right ) y^{\prime } = 0 \] |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
11.383 |
|
|
\[ {}3 t y^{2}+y^{3} y^{\prime } = 0 \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.883 |
|
|
\[ {}t -y \sin \left (t \right )+\left (y^{6}+\cos \left (t \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
3.112 |
|
|
\[ {}y \sin \left (2 t \right )+\left (\sqrt {y}+\cos \left (2 t \right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
11.048 |
|
|
\[ {}{\mathrm e}^{2 t}-y-\left ({\mathrm e}^{y}-t \right ) y^{\prime } = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.326 |
|
|
\[ {}\ln \left (t y\right )+\frac {t y^{\prime }}{y} = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
3.692 |
|
|
\[ {}{\mathrm e}^{t y}+\frac {t \,{\mathrm e}^{t y} y^{\prime }}{y} = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.963 |
|
|
\[ {}3 t^{2}-y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.203 |
|
|
\[ {}-1+3 y^{2} y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.709 |
|
|
\[ {}y^{2}+2 t y y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.162 |
|
|
|
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