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) |
|
\[ {}y^{\prime } = \frac {y+1}{t +1} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.167 |
|
|
\[ {}y^{\prime } = t^{2} y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.587 |
|
|
\[ {}y^{\prime } = t^{4} y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.699 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.259 |
|
|
\[ {}y^{\prime } = 2-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.244 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.154 |
|
|
\[ {}x^{\prime } = 1+x^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.223 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime } = \frac {t}{y} \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.332 |
|
|
\[ {}y^{\prime } = \frac {t}{t^{2} y+y} \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.818 |
|
|
\[ {}y^{\prime } = t y^{\frac {1}{3}} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.068 |
|
|
\[ {}y^{\prime } = \frac {1}{2 y+1} \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.36 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.311 |
|
|
\[ {}y^{\prime } = y \left (1-y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime } = \frac {4 t}{1+3 y^{2}} \] |
1 |
1 |
3 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
154.546 |
|
|
\[ {}v^{\prime } = t^{2} v-2-2 v+t^{2} \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime } = \frac {1}{t y+t +y+1} \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.904 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{t} y}{1+y^{2}} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.037 |
|
|
\[ {}y^{\prime } = y^{2}-4 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}w^{\prime } = \frac {w}{t} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.747 |
|
|
\[ {}y^{\prime } = \sec \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.297 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.188 |
|
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.24 |
|
|
\[ {}y^{\prime } = t^{2} y^{3} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.401 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.194 |
|
|
\[ {}y^{\prime } = \frac {t}{y-t^{2} y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.08 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.46 |
|
|
\[ {}y^{\prime } = t y^{2}+2 y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.93 |
|
|
\[ {}x^{\prime } = \frac {t^{2}}{x+t^{3} x} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.807 |
|
|
\[ {}y^{\prime } = \frac {1-y^{2}}{y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime } = \left (1+y^{2}\right ) t \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.343 |
|
|
\[ {}y^{\prime } = \frac {1}{2 y+3} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.266 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.02 |
|
|
\[ {}y^{\prime } = \frac {y^{2}+5}{y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.503 |
|
|
\[ {}y^{\prime } = t^{2}+t \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.134 |
|
|
\[ {}y^{\prime } = t^{2}+1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.157 |
|
|
\[ {}y^{\prime } = 1-2 y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.267 |
|
|
\[ {}y^{\prime } = 4 y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.139 |
|
|
\[ {}y^{\prime } = 2 y \left (1-y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.771 |
|
|
\[ {}y^{\prime } = y+t +1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.646 |
|
|
\[ {}y^{\prime } = 3 y \left (1-y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime } = 2 y-t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.857 |
|
|
\[ {}y^{\prime } = \left (y+\frac {1}{2}\right ) \left (t +y\right ) \] |
1 |
1 |
1 |
riccati |
[_Riccati] |
✓ |
✓ |
1.829 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.127 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.45 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.099 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.278 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.711 |
|
|
\[ {}S^{\prime } = S^{3}-2 S^{2}+S \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.726 |
|
|
\[ {}y^{\prime } = y^{2}+y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.515 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.265 |
|
|
\[ {}y^{\prime } = y^{3}+y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.534 |
|
|
\[ {}y^{\prime } = -t^{2}+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.132 |
|
|
\[ {}y^{\prime } = t y+t y^{2} \] |
1 |
1 |
1 |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.455 |
|
|
\[ {}y^{\prime } = t^{2}+t^{2} y \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.767 |
|
|
\[ {}y^{\prime } = t +t y \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.754 |
|
|
\[ {}y^{\prime } = t^{2}-2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.138 |
|
|
\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.468 |
|
|
\[ {}\theta ^{\prime } = 2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.107 |
|
|
\[ {}\theta ^{\prime } = \frac {11}{10}-\frac {9 \cos \left (\theta \right )}{10} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.388 |
|
|
\[ {}v^{\prime } = -\frac {v}{R C} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.605 |
|
|
\[ {}v^{\prime } = \frac {K -v}{R C} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}v^{\prime } = 2 V \left (t \right )-2 v \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.837 |
|
|
\[ {}y^{\prime } = 2 y+1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.263 |
|
|
\[ {}y^{\prime } = t -y^{2} \] |
1 |
1 |
1 |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
4.531 |
|
|
\[ {}y^{\prime } = y^{2}-4 t \] |
1 |
1 |
1 |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
6.278 |
|
|
\[ {}y^{\prime } = \sin \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.774 |
|
|
\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.837 |
|
|
\[ {}w^{\prime } = \left (3-w\right ) \left (w+1\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.522 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.847 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{\frac {2}{y}} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.63 |
|
|
\[ {}y^{\prime } = y^{2}-y^{3} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.622 |
|
|
\[ {}y^{\prime } = 2 y^{3}+t^{2} \] |
1 |
0 |
0 |
abelFirstKind |
[_Abel] |
❇ |
N/A |
0.441 |
|
|
\[ {}y^{\prime } = \sqrt {y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.447 |
|
|
\[ {}y^{\prime } = 2-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.405 |
|
|
\[ {}\theta ^{\prime } = \frac {9}{10}-\frac {11 \cos \left (\theta \right )}{10} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
2.905 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
2.234 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
3.785 |
|
|
\[ {}y^{\prime } = y \left (y-1\right ) \left (y-3\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
2.087 |
|
|
\[ {}y^{\prime } = -y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.138 |
|
|
\[ {}y^{\prime } = y^{3} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.253 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (y+1\right ) \left (t -2\right )} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.741 |
|
|
\[ {}y^{\prime } = \frac {1}{\left (y+2\right )^{2}} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime } = \frac {t}{y-2} \] |
1 |
1 |
1 |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.28 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.872 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.544 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}y^{\prime } = 3 y \left (y-2\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.235 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.588 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.245 |
|
|
\[ {}y^{\prime } = y^{2}-4 y-12 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.575 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.8 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.705 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.263 |
|
|
\[ {}y^{\prime } = \cos \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.446 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.551 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.211 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.852 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.832 |
|
|
\[ {}w^{\prime } = w \cos \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.873 |
|
|
\[ {}w^{\prime } = \left (1-w\right ) \sin \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.564 |
|
|
\[ {}y^{\prime } = \frac {1}{y-2} \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.368 |
|
|
\[ {}v^{\prime } = -v^{2}-2 v-2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.497 |
|
|
\[ {}w^{\prime } = 3 w^{3}-12 w^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.539 |
|
|
\[ {}y^{\prime } = 1+\cos \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.327 |
|
|
\[ {}y^{\prime } = \tan \left (y\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.29 |
|
|
\[ {}y^{\prime } = y \ln \left ({| y|}\right ) \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.523 |
|
|
\[ {}w^{\prime } = \left (w^{2}-2\right ) \arctan \left (w\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.748 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.923 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.293 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.586 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.615 |
|
|
\[ {}y^{\prime } = y^{2}-4 y+2 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.49 |
|
|
\[ {}y^{\prime } = y \cos \left (\frac {\pi y}{2}\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime } = y-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.533 |
|
|
\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.753 |
|
|
\[ {}y^{\prime } = y^{3}-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.621 |
|
|
\[ {}y^{\prime } = \cos \left (\frac {\pi y}{2}\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.612 |
|
|
\[ {}y^{\prime } = y^{2}-y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.345 |
|
|
\[ {}y^{\prime } = y \sin \left (\frac {\pi y}{2}\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.128 |
|
|
\[ {}y^{\prime } = y^{2}-y^{3} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.306 |
|
|
\[ {}y^{\prime } = -4 y+9 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime } = -4 y+3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.689 |
|
|
\[ {}y^{\prime } = -3 y+4 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.989 |
|
|
\[ {}y^{\prime } = 2 y+\sin \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.91 |
|
|
\[ {}y^{\prime } = 3 y-4 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.639 |
|
|
\[ {}y^{\prime } = \frac {y}{2}+4 \,{\mathrm e}^{\frac {t}{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime }+2 y = {\mathrm e}^{\frac {t}{3}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime }-2 y = 3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.96 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime }+3 y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.142 |
|
|
\[ {}y^{\prime }-2 y = 7 \,{\mathrm e}^{2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.913 |
|
|
\[ {}y^{\prime }+2 y = 3 t^{2}+2 t -1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.668 |
|
|
\[ {}y^{\prime }+2 y = t^{2}+2 t +1+{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.736 |
|
|
\[ {}y^{\prime }+y = t^{3}+\sin \left (3 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.999 |
|
|
\[ {}y^{\prime }-3 y = 2 t -{\mathrm e}^{4 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime }+y = \cos \left (2 t \right )+3 \sin \left (2 t \right )+{\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.089 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.137 |
|
|
\[ {}y^{\prime } = \frac {3 y}{t}+t^{5} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.684 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+t^{2} \] |
1 |
1 |
1 |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.833 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{\prime }-\frac {2 t y}{t^{2}+1} = 3 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.793 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = {\mathrm e}^{t} t^{3} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.738 |
|
|
\[ {}y^{\prime } = -\frac {y}{t +1}+2 \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.886 |
|
|
\[ {}y^{\prime } = \frac {y}{t +1}+4 t^{2}+4 t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.939 |
|
|
\[ {}y^{\prime } = -\frac {y}{t}+2 \] |
1 |
1 |
1 |
exact, linear, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.484 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.893 |
|
|
\[ {}y^{\prime }-\frac {2 y}{t} = 2 t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.809 |
|
|
\[ {}y^{\prime }-\frac {3 y}{t} = 2 t^{3} {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.991 |
|
|
\[ {}y^{\prime } = \sin \left (t \right ) y+4 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.56 |
|
|
\[ {}y^{\prime } = t^{2} y+4 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.383 |
|
|
\[ {}y^{\prime } = \frac {y}{t^{2}}+4 \cos \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.75 |
|
|
\[ {}y^{\prime } = y+4 \cos \left (t^{2}\right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.403 |
|
|
\[ {}y^{\prime } = -y \,{\mathrm e}^{-t^{2}}+\cos \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.383 |
|
|
\[ {}y^{\prime } = \frac {y}{\sqrt {t^{3}-3}}+t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
10.095 |
|
|
\[ {}y^{\prime } = a t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.009 |
|
|
\[ {}y^{\prime } = t^{r} y+4 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.659 |
|
|
\[ {}v^{\prime }+\frac {2 v}{5} = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.017 |
|
|
\[ {}y^{\prime } = -2 t y+4 \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.653 |
|
|
\[ {}y^{\prime }+2 y = 3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.64 |
|
|
\[ {}y^{\prime } = 3 y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime } = t^{2} \left (t^{2}+1\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.157 |
|
|
\[ {}y^{\prime } = -\sin \left (y\right )^{5} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.891 |
|
|
\[ {}y^{\prime } = \frac {\left (t^{2}-4\right ) \left (y+1\right ) {\mathrm e}^{y}}{\left (-1+t \right ) \left (3-y\right )} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.492 |
|
|
\[ {}y^{\prime } = \sin \left (y\right )^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.287 |
|
|
\[ {}y^{\prime } = \left (y-3\right ) \left (\sin \left (y\right ) \sin \left (t \right )+\cos \left (t \right )+1\right ) \] |
1 |
0 |
0 |
unknown |
[‘x=_G(y,y’)‘] |
❇ |
N/A |
3.796 |
|
|
\[ {}y^{\prime } = y+{\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.622 |
|
|
\[ {}y^{\prime } = 3-2 y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.257 |
|
|
\[ {}y^{\prime } = t y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.671 |
|
|
\[ {}y^{\prime } = 3 y+{\mathrm e}^{7 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime } = \frac {t y}{t^{2}+1} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.777 |
|
|
\[ {}y^{\prime } = -5 y+\sin \left (3 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.934 |
|
|
\[ {}y^{\prime } = t +\frac {2 y}{t +1} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.773 |
|
|
\[ {}y^{\prime } = 3+y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.214 |
|
|
\[ {}y^{\prime } = 2 y-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.271 |
|
|
\[ {}y^{\prime } = -3 y+{\mathrm e}^{-2 t}+t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.74 |
|
|
\[ {}x^{\prime } = -x t \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.101 |
|
|
\[ {}y^{\prime } = 2 y+\cos \left (4 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime } = 3 y+2 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.948 |
|
|
\[ {}y^{\prime } = t^{2} y^{3}+y^{3} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.82 |
|
|
\[ {}y^{\prime }+5 y = 3 \,{\mathrm e}^{-5 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = 2 t y+3 t \,{\mathrm e}^{t^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.978 |
|
|
\[ {}y^{\prime } = \frac {\left (t +1\right )^{2}}{\left (y+1\right )^{2}} \] |
1 |
1 |
1 |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
142.759 |
|
|
\[ {}y^{\prime } = 2 t y^{2}+3 t^{2} y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.585 |
|
|
\[ {}y^{\prime } = 1-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{y+t^{3} y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.47 |
|
|
\[ {}y^{\prime } = y^{2}-2 y+1 \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.526 |
|
|
\[ {}y^{\prime } = \left (y-2\right ) \left (y+1-\cos \left (t \right )\right ) \] |
1 |
1 |
1 |
riccati |
[_Riccati] |
✓ |
✓ |
5.055 |
|
|
\[ {}y^{\prime } = \left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \] |
1 |
0 |
0 |
abelFirstKind |
[_Abel] |
❇ |
N/A |
5.54 |
|
|
\[ {}y^{\prime } = t^{2} y+1+y+t^{2} \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.416 |
|
|
\[ {}y^{\prime } = \frac {2 y+1}{t} \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.338 |
|
|
\[ {}y^{\prime } = 3-y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.604 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.424 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.503 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.563 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.87 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 y \\ y^{\prime }=3 \pi y-\frac {x}{3} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.186 |
|
|
\[ {}\left [\begin {array}{c} p^{\prime }=3 p-2 q-7 r \\ q^{\prime }=-2 p+6 r \\ r^{\prime }=\frac {73 q}{100}+2 r \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
99.342 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+2 \pi y \\ y^{\prime }=4 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.168 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\beta y \\ y^{\prime }=\gamma x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.895 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x-y \\ y^{\prime }=x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.487 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=2 x-5 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.583 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-3 y \\ y^{\prime }=3 x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.656 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+3 y \\ y^{\prime }=x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=1 \\ y^{\prime }=x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.517 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.435 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x-2 y \\ y^{\prime }=-x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.615 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-5 x-2 y \\ y^{\prime }=-x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.62 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.598 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {x}{2} \\ y^{\prime }=x-\frac {y}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=5 x+4 y \\ y^{\prime }=9 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.654 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+4 y \\ y^{\prime }=x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.829 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.771 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x-2 y \\ y^{\prime }=x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.605 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.667 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.595 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-2 y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.534 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.525 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.565 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.559 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+y \\ y^{\prime }=2 x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.513 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.467 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x-2 y \\ y^{\prime }=x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.522 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.575 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.311 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.381 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.375 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.855 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.562 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+2 y \\ y^{\prime }=-4 x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x-5 y \\ y^{\prime }=3 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.742 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.76 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-6 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.741 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+4 y \\ y^{\prime }=-3 x+2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.732 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-\frac {9 x}{10}-2 y \\ y^{\prime }=x+\frac {11 y}{10} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.708 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+10 y \\ y^{\prime }=-x+3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.776 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.441 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.933 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.49 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.504 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x \\ y^{\prime }=x-3 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.413 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+y \\ y^{\prime }=-x+4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.462 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x-y \\ y^{\prime }=x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.433 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.438 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.437 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x+4 y \\ y^{\prime }=3 x+6 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.518 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=4 x+2 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.499 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 y \\ y^{\prime }=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.369 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 y \\ y^{\prime }=0 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.375 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x-y \\ y^{\prime }=4 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.525 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }-7 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.366 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-12 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.358 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\frac {y}{10} \\ y^{\prime }=\frac {z}{5} \\ z^{\prime }=\frac {2 x}{5} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.663 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-x \\ z^{\prime }=2 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.908 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+3 y \\ y^{\prime }=3 x-2 y \\ z^{\prime }=-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.783 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+3 z \\ y^{\prime }=-y \\ z^{\prime }=-3 x+z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.997 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x \\ y^{\prime }=2 y-z \\ z^{\prime }=-y+2 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.53 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.467 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y \\ z^{\prime }=z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.466 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+2 y \\ y^{\prime }=2 x-4 y \\ z^{\prime }=0 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.657 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-2 x+y \\ y^{\prime }=-2 y+z \\ z^{\prime }=-2 z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.465 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=z \\ z^{\prime }=0 \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.48 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x-y \\ y^{\prime }=-2 y+3 z \\ z^{\prime }=-x+3 y-z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.845 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-4 x+3 y \\ y^{\prime }=-y+z \\ z^{\prime }=5 x-5 y \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.633 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-10 x+10 y \\ y^{\prime }=28 x-y \\ z^{\prime }=-\frac {8 z}{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.366 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y+z \\ y^{\prime }=-x+z \\ z^{\prime }=z \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.792 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 0 & 2 \end {array}\right ]\) |
|
|
|
Eigenvectors |
N/A |
✓ |
N/A |
0.174 |
|
|
\(\left [\begin {array}{cc} 0 & 1 \\ 2 & 0 \end {array}\right ]\) |
|
|
|
Eigenvectors |
N/A |
✓ |
N/A |
0.285 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x \\ y^{\prime }=-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.433 |
|
|
\(\left [\begin {array}{cc} 1 & 0 \\ 2 & 3 \end {array}\right ]\) |
|
|
|
Eigenvectors |
N/A |
✓ |
N/A |
0.189 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=0 \\ y^{\prime }=x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.46 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=\pi ^{2} x+\frac {187 y}{5} \\ y^{\prime }=\sqrt {555}\, x+\frac {400617 y}{5000} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.509 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=x+y \\ y^{\prime }=-2 x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.754 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.854 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x+y \\ y^{\prime }=-x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.878 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x+y \\ y^{\prime }=-2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.735 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=2 x \\ y^{\prime }=x-y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.3 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=3 x+y \\ y^{\prime }=-x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.468 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=y \\ y^{\prime }=-4 x-4 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.376 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-3 x-3 y \\ y^{\prime }=2 x+y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.933 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.478 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.633 |
|
|
\[ {}y^{\prime \prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
5.259 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-6 y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.419 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.429 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 5 \,{\mathrm e}^{3 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.421 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.695 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.519 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = {\mathrm e}^{4 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.459 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-6 y = 4 \,{\mathrm e}^{-3 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.659 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+12 y = 3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.664 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = -3 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.725 |
|
|
\[ {}y^{\prime \prime }+7 y^{\prime }+10 y = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.731 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-\frac {t}{2}} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.694 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.631 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-\frac {t}{2}} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.03 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.856 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-4 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.805 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.487 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+4 y = 5 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.639 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 2 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.617 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+10 y = 10 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.859 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 y = -8 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.246 |
|
|
\[ {}y^{\prime \prime }+9 y = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.798 |
|
|
\[ {}y^{\prime \prime }+4 y = 2 \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.794 |
|
|
\[ {}y^{\prime \prime }+2 y = -3 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.763 |
|
|
\[ {}y^{\prime \prime }+4 y = {\mathrm e}^{t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.709 |
|
|
\[ {}y^{\prime \prime }+9 y = 6 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.707 |
|
|
\[ {}y^{\prime \prime }+2 y = -{\mathrm e}^{t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.073 |
|
|
\[ {}y^{\prime \prime }+4 y = -3 t^{2}+2 t +3 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.888 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime } = 3 t +2 \] |
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]] |
✓ |
✓ |
2.078 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime } = 3 t +2 \] |
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]] |
✓ |
✓ |
2.102 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = t^{2} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.691 |
|
|
\[ {}y^{\prime \prime }+4 y = t -\frac {1}{20} t^{2} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.879 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 4+{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.701 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{-t}-4 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.706 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.717 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 t +{\mathrm e}^{t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.714 |
|
|
\[ {}y^{\prime \prime }+4 y = t +{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.844 |
|
|
\[ {}y^{\prime \prime }+4 y = 6+t^{2}+{\mathrm e}^{t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.958 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.509 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 5 \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.498 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 2 \sin \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.452 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.493 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = -4 \cos \left (3 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.553 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+13 y = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.849 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -\cos \left (5 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.064 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.901 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = \cos \left (3 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.707 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.742 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+8 y = 2 \cos \left (3 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.778 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+20 y = -3 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.94 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 2 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.108 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+y = \cos \left (3 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.755 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = 3+2 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+20 y = {\mathrm e}^{-t} \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.785 |
|
|
\[ {}y^{\prime \prime }+9 y = \cos \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.794 |
|
|
\[ {}y^{\prime \prime }+9 y = 5 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.715 |
|
|
\[ {}y^{\prime \prime }+4 y = -\cos \left (\frac {t}{2}\right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.859 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.643 |
|
|
\[ {}y^{\prime \prime }+9 y = 2 \cos \left (3 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.651 |
|
|
\[ {}y^{\prime \prime }+4 y = 8 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.468 |
|
|
\[ {}y^{\prime \prime }-4 y = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.497 |
|
|
\[ {}y^{\prime \prime }-4 y^{\prime }+5 y = 2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.613 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 13 \operatorname {Heaviside}\left (t -4\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.898 |
|
|
\[ {}y^{\prime \prime }+4 y = \cos \left (2 t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.609 |
|
|
\[ {}y^{\prime \prime }+3 y = \operatorname {Heaviside}\left (t -4\right ) \cos \left (5 t -20\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.593 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+9 y = 20 \operatorname {Heaviside}\left (t -2\right ) \sin \left (t -2\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.691 |
|
|
\[ {}y^{\prime \prime }+3 y = \left \{\begin {array}{cc} t & 0\le t <1 \\ 1 & 1\le t \end {array}\right . \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.58 |
|
|
\[ {}y^{\prime \prime }+3 y = 5 \delta \left (t -2\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.171 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+5 y = \delta \left (t -3\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.632 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = -2 \delta \left (t -2\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.563 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+3 y = \delta \left (-1+t \right )-3 \delta \left (t -4\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
5.292 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = \sin \left (4 t \right ) {\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.986 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+5 y = \operatorname {Heaviside}\left (t -2\right ) \sin \left (4 t -8\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
3.886 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+8 y = \left (1-\operatorname {Heaviside}\left (t -4\right )\right ) \cos \left (t -4\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.871 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+3 y = \left (1-\operatorname {Heaviside}\left (t -2\right )\right ) {\mathrm e}^{-\frac {t}{10}+\frac {1}{5}} \sin \left (t -2\right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
4.797 |
|
|
\[ {}y^{\prime \prime }+16 y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime }+4 y = \sin \left (2 t \right ) \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.676 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.38 |
|
|
\[ {}y^{\prime \prime }+16 y = t \] |
1 |
1 |
1 |
second_order_laplace |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.548 |
|
|
|
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