|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.736 |
|
|
\[ {}y^{\prime }+y = t^{3}+\sin \left (3 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.999 |
|
|
\[ {}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.089 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+t^{2} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = t^{3} {\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+2 \] |
exact, linear, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.484 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = 2 t^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.991 |
|
|
\[ {}y^{\prime } = \sin \left (t \right ) y+4 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.56 |
|
|
\[ {}y^{\prime } = t^{2} y+4 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = y+4 \cos \left (t^{2}\right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.403 |
|
|
\[ {}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.383 |
|
|
\[ {}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
10.095 |
|
|
\[ {}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.009 |
|
|
\[ {}y^{\prime } = t^{r} y+4 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.659 |
|
|
\[ {}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.017 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime } = 3 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime } = t^{2} \left (t^{2}+1\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.157 |
|
|
\[ {}y^{\prime } = -\sin \left (y\right )^{5} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.891 |
|
|
\[ {}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.492 |
|
|
\[ {}y^{\prime } = \sin \left (y\right )^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.287 |
|
|
\[ {}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \] |
unknown |
[‘x=_G(y,y’)‘] |
❇ |
N/A |
3.796 |
|
|
\[ {}y^{\prime } = y+{\mathrm e}^{-t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.622 |
|
|
\[ {}y^{\prime } = 3-2 y \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.257 |
|
|
\[ {}y^{\prime } = t y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime } = 3 y+{\mathrm e}^{7 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.777 |
|
|
\[ {}y^{\prime } = -5 y+\sin \left (3 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.934 |
|
|
\[ {}y^{\prime } = t +\frac {2 y}{t +1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.773 |
|
|
\[ {}y^{\prime } = 3+y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.214 |
|
|
\[ {}y^{\prime } = 2 y-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.271 |
|
|
\[ {}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.74 |
|
|
\[ {}x^{\prime } = -x t \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.101 |
|
|
\[ {}y^{\prime } = 2 y+\cos \left (4 t \right ) \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.82 |
|
|
\[ {}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.978 |
|
|
\[ {}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}} \] |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
142.759 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = 1-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{y+t^{3} y} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.47 |
|
|
\[ {}y^{\prime } = y^{2}-2 y+1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
5.055 |
|
|
\[ {}y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \] |
abelFirstKind |
[_Abel] |
❇ |
N/A |
5.54 |
|
|
\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.416 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.338 |
|
|
\[ {}y^{\prime } = 3-y^{2} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.604 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.424 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.503 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.563 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.87 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.186 |
|
|
\[ {}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
99.342 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.168 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.895 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.487 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.583 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.656 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.435 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.615 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.598 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.829 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.771 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.667 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.595 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.534 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.525 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.565 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.559 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.513 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.467 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.575 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.311 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.381 |
|
|
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