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) |
|
\[ {}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.835 |
|
|
\[ {}y^{\prime }+y = 1+t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.87 |
|
|
\[ {}\frac {y}{t}+y^{\prime } = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.093 |
|
|
\[ {}-2 y+y^{\prime } = 3 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.859 |
|
|
\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.026 |
|
|
\[ {}2 t y+y^{\prime } = 2 t \,{\mathrm e}^{-t^{2}} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.909 |
|
|
\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = \frac {1}{\left (t^{2}+1\right )^{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.116 |
|
|
\[ {}y+2 y^{\prime } = 3 t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.829 |
|
|
\[ {}-y+t y^{\prime } = t^{2} {\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.972 |
|
|
\[ {}y^{\prime }+y = 5 \sin \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.095 |
|
|
\[ {}y+2 y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.847 |
|
|
\[ {}-y+y^{\prime } = 2 \,{\mathrm e}^{2 t} t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.323 |
|
|
\[ {}2 y+y^{\prime } = t \,{\mathrm e}^{-2 t} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.334 |
|
|
\[ {}2 y+t y^{\prime } = t^{2}-t +1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.304 |
|
|
\[ {}\frac {2 y}{t}+y^{\prime } = \frac {\cos \left (t \right )}{t^{2}} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.337 |
|
|
\[ {}-2 y+y^{\prime } = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.156 |
|
|
\[ {}2 y+t y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.485 |
|
|
\[ {}4 t^{2} y+t^{3} y^{\prime } = {\mathrm e}^{-t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.281 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.574 |
|
|
\[ {}-\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.368 |
|
|
\[ {}-y+2 y^{\prime } = {\mathrm e}^{\frac {t}{3}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.177 |
|
|
\[ {}-2 y+3 y^{\prime } = {\mathrm e}^{-\frac {\pi t}{2}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.498 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = 2 t \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.252 |
|
|
\[ {}2 y+t y^{\prime } = \frac {\sin \left (t \right )}{t} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.239 |
|
|
\[ {}\cos \left (t \right ) y+\sin \left (t \right ) y^{\prime } = {\mathrm e}^{t} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
33.713 |
|
|
\[ {}\frac {y}{2}+y^{\prime } = 2 \cos \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.518 |
|
|
\[ {}\frac {2 y}{3}+y^{\prime } = -\frac {t}{2}+1 \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.88 |
|
|
\[ {}\frac {y}{4}+y^{\prime } = 3+2 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.701 |
|
|
\[ {}-y+y^{\prime } = 1+3 \sin \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.127 |
|
|
\[ {}-\frac {3 y}{2}+y^{\prime } = 2 \,{\mathrm e}^{t}+3 t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.044 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{y} \] |
1 |
1 |
2 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.209 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{\left (x^{3}+1\right ) y} \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.006 |
|
|
\[ {}\sin \left (x \right ) y^{2}+y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-1}{3+2 y} \] |
1 |
1 |
2 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.528 |
|
|
\[ {}y^{\prime } = \cos \left (x \right )^{2} \cos \left (2 y\right )^{2} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.35 |
|
|
\[ {}x y^{\prime } = \sqrt {1-y^{2}} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.28 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{-x}+x}{{\mathrm e}^{y}+x} \] |
1 |
0 |
0 |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
1.497 |
|
|
\[ {}y^{\prime } = \frac {x^{2}}{1+y^{2}} \] |
1 |
1 |
3 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
154.618 |
|
|
\[ {}y^{\prime } = \left (1-2 x \right ) y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.166 |
|
|
\[ {}y^{\prime } = \frac {1-2 x}{y} \] |
1 |
1 |
1 |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.71 |
|
|
\[ {}x +y y^{\prime } {\mathrm e}^{-x} = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.847 |
|
|
\[ {}r^{\prime } = \frac {r^{2}}{x} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.269 |
|
|
\[ {}y^{\prime } = \frac {2 x}{y+x^{2} y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.673 |
|
|
\[ {}y^{\prime } = \frac {x y^{2}}{\sqrt {x^{2}+1}} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.391 |
|
|
\[ {}y^{\prime } = \frac {2 x}{2 y+1} \] |
1 |
1 |
1 |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.693 |
|
|
\[ {}y^{\prime } = \frac {x \left (x^{2}+1\right )}{4 y^{3}} \] |
1 |
1 |
1 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.85 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.863 |
|
|
\[ {}y^{\prime } = \frac {{\mathrm e}^{-x}-{\mathrm e}^{x}}{3+4 y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.872 |
|
|
\[ {}\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
10.198 |
|
|
\[ {}\sqrt {-x^{2}+1}\, y^{2} y^{\prime } = \arcsin \left (x \right ) \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.728 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}+1}{-6 y+3 y^{2}} \] |
1 |
1 |
1 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.06 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}}{-4+3 y^{2}} \] |
1 |
1 |
1 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
78.154 |
|
|
\[ {}y^{\prime } = 2 y^{2}+x y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.219 |
|
|
\[ {}y^{\prime } = \frac {2-{\mathrm e}^{x}}{3+2 y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.759 |
|
|
\[ {}y^{\prime } = \frac {2 \cos \left (2 x \right )}{3+2 y} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.18 |
|
|
\[ {}y^{\prime } = 2 \left (1+x \right ) \left (1+y^{2}\right ) \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.824 |
|
|
\[ {}y^{\prime } = \frac {t \left (4-y\right ) y}{3} \] |
1 |
1 |
1 |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.697 |
|
|
\[ {}y^{\prime } = \frac {t y \left (4-y\right )}{t +1} \] |
1 |
1 |
1 |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.964 |
|
|
\[ {}y^{\prime } = \frac {a y+b}{d +c y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.796 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+x y+y^{2}}{x^{2}} \] |
1 |
1 |
1 |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.453 |
|
|
\[ {}y^{\prime } = \frac {x^{2}+3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.633 |
|
|
\[ {}y^{\prime } = \frac {4 y-3 x}{2 x -y} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.151 |
|
|
\[ {}y^{\prime } = -\frac {4 x +3 y}{y+2 x} \] |
1 |
1 |
9 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.331 |
|
|
\[ {}y^{\prime } = \frac {x +3 y}{x -y} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.486 |
|
|
\[ {}x^{2}+3 x y+y^{2}-x^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
riccati, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
1.265 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-3 y^{2}}{2 x y} \] |
1 |
1 |
2 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.742 |
|
|
\[ {}y^{\prime } = \frac {3 y^{2}-x^{2}}{2 x y} \] |
1 |
1 |
2 |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.518 |
|
|
\[ {}\ln \left (t \right ) y+\left (t -3\right ) y^{\prime } = 2 t \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
3.69 |
|
|
\[ {}y+\left (t -4\right ) t y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.551 |
|
|
\[ {}\tan \left (t \right ) y+y^{\prime } = \sin \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.693 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.746 |
|
|
\[ {}2 t y+\left (-t^{2}+4\right ) y^{\prime } = 3 t^{2} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.372 |
|
|
\[ {}y+\ln \left (t \right ) y^{\prime } = \cot \left (t \right ) \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.854 |
|
|
\[ {}y^{\prime } = \frac {t^{2}+1}{3 y-y^{2}} \] |
1 |
1 |
3 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
168.757 |
|
|
\[ {}y^{\prime } = \frac {\cot \left (t \right ) y}{y+1} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.37 |
|
|
\[ {}y^{\prime } = -\frac {4 t}{y} \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.775 |
|
|
\[ {}y^{\prime } = 2 t y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.711 |
|
|
\[ {}y^{3}+y^{\prime } = 0 \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.434 |
|
|
\[ {}y^{\prime } = \frac {t^{2}}{\left (t^{3}+1\right ) y} \] |
1 |
1 |
2 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.052 |
|
|
\[ {}y^{\prime } = t \left (3-y\right ) y \] |
1 |
1 |
1 |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.431 |
|
|
\[ {}y^{\prime } = y \left (3-t y\right ) \] |
1 |
1 |
1 |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.845 |
|
|
\[ {}y^{\prime } = -y \left (3-t y\right ) \] |
1 |
1 |
1 |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.822 |
|
|
\[ {}y^{\prime } = t -1-y^{2} \] |
1 |
1 |
1 |
riccati |
[_Riccati] |
✓ |
✓ |
1.582 |
|
|
\[ {}y^{\prime } = a y+b y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.655 |
|
|
\[ {}y^{\prime } = y \left (-2+y\right ) \left (-1+y\right ) \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
1.938 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.542 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{-y} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.531 |
|
|
\[ {}y^{\prime } = -\frac {2 \arctan \left (y\right )}{1+y^{2}} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
3.049 |
|
|
\[ {}y^{\prime } = -k \left (-1+y\right )^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.24 |
|
|
\[ {}y^{\prime } = y^{2} \left (y^{2}-1\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.505 |
|
|
\[ {}y^{\prime } = y \left (1-y^{2}\right ) \] |
1 |
2 |
2 |
quadrature |
[_quadrature] |
✓ |
✓ |
2.153 |
|
|
\[ {}y^{\prime } = -b \sqrt {y}+a y \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.737 |
|
|
\[ {}y^{\prime } = y^{2} \left (4-y^{2}\right ) \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.51 |
|
|
\[ {}y^{\prime } = \left (1-y\right )^{2} y^{2} \] |
1 |
1 |
1 |
quadrature |
[_quadrature] |
✓ |
✓ |
0.559 |
|
|
\[ {}3+2 x +\left (-2+2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.759 |
|
|
\[ {}2 x +4 y+\left (2 x -2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.393 |
|
|
\[ {}2+3 x^{2}-2 x y+\left (3-x^{2}+6 y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact, differentialType |
[_exact, _rational] |
✓ |
✓ |
18.126 |
|
|
\[ {}2 y+2 x y^{2}+\left (2 x +2 x^{2} y\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.071 |
|
|
\[ {}y^{\prime } = \frac {-x a -b y}{b x +c y} \] |
1 |
1 |
2 |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.531 |
|
|
\[ {}y^{\prime } = \frac {-x a +b y}{b x -c y} \] |
1 |
1 |
1 |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.492 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )-2 \sin \left (x \right ) y+\left (2 \cos \left (x \right )+{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact] |
✓ |
✓ |
10.509 |
|
|
\[ {}{\mathrm e}^{x} \sin \left (y\right )+3 y-\left (3 x -{\mathrm e}^{x} \sin \left (y\right )\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[‘x=_G(y,y’)‘] |
❇ |
N/A |
7.641 |
|
|
\[ {}2 x -2 \,{\mathrm e}^{x y} \sin \left (2 x \right )+{\mathrm e}^{x y} \cos \left (2 x \right ) y+\left (-3+{\mathrm e}^{x y} x \cos \left (2 x \right )\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact] |
✓ |
✓ |
9.246 |
|
|
\[ {}\frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.185 |
|
|
\[ {}x \ln \left (x \right )+x y+\left (y \ln \left (x \right )+x y\right ) y^{\prime } = 0 \] |
1 |
0 |
0 |
unknown |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
1.007 |
|
|
\[ {}\frac {x}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{\frac {3}{2}}} = 0 \] |
1 |
1 |
2 |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.527 |
|
|
\[ {}2 x -y+\left (-x +2 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.914 |
|
|
\[ {}-1+9 x^{2}+y+\left (x -4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
8.075 |
|
|
\[ {}x^{2} y^{3}+x \left (1+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.512 |
|
|
\[ {}y+\left (2 x -{\mathrm e}^{y} y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.762 |
|
|
\[ {}\left (2+x \right ) \sin \left (y\right )+x \cos \left (y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.997 |
|
|
\[ {}2 x y+3 x^{2} y+y^{3}+\left (x^{2}+y^{2}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
homogeneousTypeD2, exactWithIntegrationFactor |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
3.155 |
|
|
\[ {}y^{\prime } = -1+{\mathrm e}^{2 x}+y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.841 |
|
|
\[ {}1+\left (-\sin \left (y\right )+\frac {x}{y}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.234 |
|
|
\[ {}y+\left (-{\mathrm e}^{-2 y}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
2.399 |
|
|
\[ {}{\mathrm e}^{x}+\left ({\mathrm e}^{x} \cot \left (y\right )+2 \csc \left (y\right ) y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
3.892 |
|
|
\[ {}\frac {4 x^{3}}{y^{2}}+\frac {3}{y}+\left (\frac {3 x}{y^{2}}+4 y\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[_rational] |
✓ |
✓ |
2.105 |
|
|
\[ {}3 x +\frac {6}{y}+\left (\frac {x^{2}}{y}+\frac {3 y}{x}\right ) y^{\prime } = 0 \] |
1 |
1 |
3 |
exact, differentialType |
[_rational] |
✓ |
✓ |
14.87 |
|
|
\[ {}3 x y+y^{2}+\left (x^{2}+x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.201 |
|
|
\[ {}y^{\prime } = \frac {x^{3}-2 y}{x} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.846 |
|
|
\[ {}y^{\prime } = \frac {\cos \left (x \right )+1}{2-\sin \left (y\right )} \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.089 |
|
|
\[ {}y^{\prime } = \frac {y+2 x}{3-x +3 y^{2}} \] |
1 |
1 |
1 |
exact, differentialType |
[_rational] |
✓ |
✓ |
280.432 |
|
|
\[ {}y^{\prime } = 3-6 x +y-2 x y \] |
1 |
1 |
1 |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.21 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y-y^{2}}{x^{2}+2 x y} \] |
1 |
1 |
2 |
exact |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.851 |
|
|
\[ {}x y+x y^{\prime } = 1-y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.539 |
|
|
\[ {}y^{\prime } = \frac {4 x^{3}+1}{y \left (2+3 y\right )} \] |
1 |
1 |
3 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
89.541 |
|
|
\[ {}2 y+x y^{\prime } = \frac {\sin \left (x \right )}{x} \] |
1 |
1 |
1 |
exact, linear, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.504 |
|
|
\[ {}y^{\prime } = \frac {-1-2 x y}{x^{2}+2 y} \] |
1 |
1 |
2 |
exact, differentialType |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.277 |
|
|
\[ {}\frac {-x^{2}+x +1}{x^{2}}+\frac {y y^{\prime }}{y-2} = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.885 |
|
|
\[ {}x^{2}+y+\left ({\mathrm e}^{y}+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType |
[_exact] |
✓ |
✓ |
3.525 |
|
|
\[ {}y+y^{\prime } = \frac {1}{1+{\mathrm e}^{x}} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.929 |
|
|
\[ {}y^{\prime } = 1+2 x +y^{2}+2 x y^{2} \] |
1 |
1 |
1 |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.109 |
|
|
\[ {}x +y+\left (2 y+x \right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
6.832 |
|
|
\[ {}\left (1+{\mathrm e}^{x}\right ) y^{\prime } = y-{\mathrm e}^{x} y \] |
1 |
1 |
1 |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.78 |
|
|
\[ {}y^{\prime } = \frac {-{\mathrm e}^{2 y} \cos \left (x \right )+\cos \left (y\right ) {\mathrm e}^{-x}}{2 \,{\mathrm e}^{2 y} \sin \left (x \right )-\sin \left (y\right ) {\mathrm e}^{-x}} \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[NONE] |
✓ |
✓ |
48.562 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{2 x}+3 y \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
0.88 |
|
|
\[ {}2 y+y^{\prime } = {\mathrm e}^{-x^{2}-2 x} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.011 |
|
|
\[ {}y^{\prime } = \frac {3 x^{2}-2 y-y^{3}}{2 x +3 x y^{2}} \] |
1 |
1 |
3 |
exact |
[_rational] |
✓ |
✓ |
2.016 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{x +y} \] |
1 |
1 |
1 |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.915 |
|
|
\[ {}\frac {-4+6 x y+2 y^{2}}{3 x^{2}+4 x y+3 y^{2}}+y^{\prime } = 0 \] |
1 |
1 |
3 |
exact |
[_rational] |
✓ |
✓ |
2.35 |
|
|
\[ {}y^{\prime } = \frac {x^{2}-1}{1+y^{2}} \] |
1 |
1 |
1 |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
67.306 |
|
|
\[ {}\left (t +1\right ) y+t y^{\prime } = {\mathrm e}^{2 t} \] |
1 |
1 |
1 |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.082 |
|
|
\[ {}2 \cos \left (x \right ) \sin \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \sin \left (x \right )^{2} y^{\prime } = 0 \] |
1 |
1 |
1 |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.416 |
|
|
\[ {}\frac {2 x}{y}-\frac {y}{x^{2}+y^{2}}+\left (-\frac {x^{2}}{y^{2}}+\frac {x}{x^{2}+y^{2}}\right ) y^{\prime } = 0 \] |
1 |
1 |
1 |
exact |
[_exact, _rational] |
✓ |
✓ |
2.711 |
|
|
\[ {}x y^{\prime } = {\mathrm e}^{\frac {y}{x}} x +y \] |
1 |
1 |
1 |
homogeneousTypeD, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.954 |
|
|
\[ {}y^{\prime } = \frac {x}{x^{2}+y+y^{3}} \] |
1 |
1 |
1 |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.819 |
|
|
\[ {}3 t +2 y = -t y^{\prime } \] |
1 |
1 |
1 |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.25 |
|
|
\[ {}y^{\prime } = \frac {x +y}{x -y} \] |
1 |
1 |
1 |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.519 |
|
|
\[ {}2 x y+3 y^{2}-\left (x^{2}+2 x y\right ) y^{\prime } = 0 \] |
1 |
1 |
2 |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.812 |
|
|
\[ {}y^{\prime } = \frac {-3 x^{2} y-y^{2}}{2 x^{3}+3 x y} \] |
1 |
1 |
1 |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.122 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.317 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.315 |
|
|
\[ {}6 y^{\prime \prime }-y^{\prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.344 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.334 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime } = 0 \] |
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_x]] |
✓ |
✓ |
1.044 |
|
|
\[ {}4 y^{\prime \prime }-9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.247 |
|
|
\[ {}y^{\prime \prime }-9 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.408 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.398 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.643 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.707 |
|
|
\[ {}6 y^{\prime \prime }-5 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.693 |
|
|
\[ {}y^{\prime \prime }+3 y^{\prime } = 0 \] |
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_x]] |
✓ |
✓ |
2.002 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.239 |
|
|
\[ {}2 y^{\prime \prime }+y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.194 |
|
|
\[ {}y^{\prime \prime }+8 y^{\prime }-9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.835 |
|
|
\[ {}4 y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.715 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.232 |
|
|
\[ {}2 y^{\prime \prime }-3 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.663 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.593 |
|
|
\[ {}4 y^{\prime \prime }-y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
2.939 |
|
|
\[ {}y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (\alpha -1\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.376 |
|
|
\[ {}y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.503 |
|
|
\[ {}2 y^{\prime \prime }+3 y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.644 |
|
|
\[ {}y^{\prime \prime }+5 y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.592 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.424 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.645 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }-8 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.32 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.431 |
|
|
\[ {}y^{\prime \prime }+6 y^{\prime }+13 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.542 |
|
|
\[ {}4 y^{\prime \prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.548 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+\frac {5 y}{4} = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.511 |
|
|
\[ {}9 y^{\prime \prime }+9 y^{\prime }-4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.348 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.511 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+\frac {25 y}{4} = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.561 |
|
|
\[ {}y^{\prime \prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
3.127 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.847 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+5 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.204 |
|
|
\[ {}y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
6.435 |
|
|
\[ {}y^{\prime \prime }+y^{\prime }+\frac {5 y}{4} = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.851 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+2 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.181 |
|
|
\[ {}u^{\prime \prime }-u^{\prime }+2 u = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.443 |
|
|
\[ {}5 u^{\prime \prime }+2 u^{\prime }+7 u = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.72 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.169 |
|
|
\[ {}y^{\prime \prime }+2 a y^{\prime }+\left (a^{2}+1\right ) y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.953 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.654 |
|
|
\[ {}t^{2} y^{\prime \prime }+4 t y^{\prime }+2 y = 0 \] |
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_1, second_order_change_of_variable_on_y_method_2, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.901 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+\frac {5 y}{4} = 0 \] |
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]] |
✓ |
✓ |
1.946 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }-6 y = 0 \] |
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_2, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.383 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \] |
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 |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.827 |
|
|
\[ {}t^{2} y^{\prime \prime }-t y^{\prime }+5 y = 0 \] |
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]] |
✓ |
✓ |
1.928 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }-3 y = 0 \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.738 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+10 y = 0 \] |
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]] |
✓ |
✓ |
1.929 |
|
|
\[ {}y^{\prime \prime }+t y^{\prime }+{\mathrm e}^{-t^{2}} y = 0 \] |
1 |
1 |
1 |
second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2 |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.97 |
|
|
\[ {}t y^{\prime \prime }+\left (t^{2}-1\right ) y^{\prime }+t^{3} y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_change_of_variable_on_x_method_1, second_order_change_of_variable_on_x_method_2 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.348 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.391 |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.425 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }-3 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.346 |
|
|
\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.432 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+10 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.558 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.401 |
|
|
\[ {}4 y^{\prime \prime }+17 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.353 |
|
|
\[ {}16 y^{\prime \prime }+24 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.435 |
|
|
\[ {}25 y^{\prime \prime }-20 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.431 |
|
|
\[ {}2 y^{\prime \prime }+2 y^{\prime }+y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.524 |
|
|
\[ {}9 y^{\prime \prime }-12 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.944 |
|
|
\[ {}y^{\prime \prime }-6 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.889 |
|
|
\[ {}9 y^{\prime \prime }+6 y^{\prime }+82 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.056 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.086 |
|
|
\[ {}4 y^{\prime \prime }+12 y^{\prime }+9 y = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.984 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }+\frac {y}{4} = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.734 |
|
|
\[ {}t^{2} y^{\prime \prime }-4 t y^{\prime }+6 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.454 |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }-2 y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.44 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.449 |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.625 |
|
|
\[ {}x y^{\prime \prime }-y^{\prime }+4 x^{3} y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
0.77 |
|
|
\[ {}\left (-1+x \right ) y^{\prime \prime }-x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.718 |
|
|
\[ {}x^{2} y^{\prime \prime }-\left (x -\frac {3}{16}\right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.54 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = 0 \] |
1 |
1 |
1 |
reduction_of_order |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.675 |
|
|
\[ {}t^{2} y^{\prime \prime }-3 t y^{\prime }+4 y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.671 |
|
|
\[ {}t^{2} y^{\prime \prime }+2 t y^{\prime }+\frac {y}{4} = 0 \] |
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]] |
✓ |
✓ |
1.64 |
|
|
\[ {}2 t^{2} y^{\prime \prime }-5 t y^{\prime }+5 y = 0 \] |
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, second_order_ode_non_constant_coeff_transformation_on_B |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.15 |
|
|
\[ {}t^{2} y^{\prime \prime }+3 t y^{\prime }+y = 0 \] |
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, _homogeneous]] |
✓ |
✓ |
2.599 |
|
|
\[ {}4 t^{2} y^{\prime \prime }-8 t y^{\prime }+9 y = 0 \] |
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]] |
✓ |
✓ |
1.682 |
|
|
\[ {}t^{2} y^{\prime \prime }+5 t y^{\prime }+13 y = 0 \] |
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]] |
✓ |
✓ |
1.961 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = 2 \,{\mathrm e}^{t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.577 |
|
|
\[ {}y^{\prime \prime }-y^{\prime }-2 y = 2 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.633 |
|
|
\[ {}y^{\prime \prime }+2 y^{\prime }+y = 3 \,{\mathrm e}^{-t} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.74 |
|
|
\[ {}4 y^{\prime \prime }-4 y^{\prime }+y = 16 \,{\mathrm e}^{\frac {t}{2}} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.742 |
|
|
\[ {}y^{\prime \prime }+y = \tan \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.956 |
|
|
\[ {}y^{\prime \prime }+9 y = 9 \sec \left (3 t \right )^{2} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.793 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+4 y = \frac {{\mathrm e}^{-2 t}}{t^{2}} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.862 |
|
|
\[ {}y^{\prime \prime }+4 y = 3 \csc \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.995 |
|
|
\[ {}y^{\prime \prime }+y = 2 \sec \left (\frac {t}{2}\right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.221 |
|
|
\[ {}y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{t}}{t^{2}+1} \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, linear_second_order_ode_solved_by_an_integrating_factor |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
0.891 |
|
|
\[ {}y^{\prime \prime }-5 y^{\prime }+6 y = g \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.067 |
|
|
\[ {}y^{\prime \prime }+4 y = g \left (t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.255 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 y = 3 t^{2}-1 \] |
1 |
1 |
1 |
kovacic, second_order_euler_ode, exact linear second order ode, second_order_integrable_as_is |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
1.947 |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (2+t \right ) y^{\prime }+\left (2+t \right ) y = 2 t^{3} \] |
1 |
1 |
1 |
kovacic, second_order_change_of_variable_on_y_method_1, second_order_change_of_variable_on_y_method_2 |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.659 |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2} \] |
1 |
1 |
1 |
kovacic, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.428 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right )^{2} {\mathrm e}^{-t} \] |
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]] |
✓ |
✓ |
2.265 |
|
|
\[ {}x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y = \ln \left (x \right ) x^{2} \] |
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 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.91 |
|
|
\[ {}x^{2} y^{\prime \prime }+x y^{\prime }+\left (x^{2}-\frac {1}{4}\right ) y = g \left (x \right ) \] |
1 |
1 |
1 |
kovacic, second_order_bessel_ode, second_order_change_of_variable_on_y_method_1 |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.777 |
|
|
\[ {}t^{2} y^{\prime \prime }-2 t y^{\prime }+2 y = 4 t^{2} \] |
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, linear_second_order_ode_solved_by_an_integrating_factor, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.562 |
|
|
\[ {}t^{2} y^{\prime \prime }+7 t y^{\prime }+5 y = t \] |
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]] |
✓ |
✓ |
3.5 |
|
|
\[ {}t y^{\prime \prime }-\left (t +1\right ) y^{\prime }+y = {\mathrm e}^{2 t} t^{2} \] |
1 |
1 |
1 |
kovacic, second_order_ode_non_constant_coeff_transformation_on_B |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.213 |
|
|
\[ {}\left (1-t \right ) y^{\prime \prime }+t y^{\prime }-y = 2 \left (-1+t \right ) {\mathrm e}^{-t} \] |
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]] |
✓ |
✓ |
2.074 |
|
|
\[ {}u^{\prime \prime }+2 u = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff, second_order_ode_can_be_made_integrable |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.872 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{4}+2 u = 0 \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
1.484 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (\frac {t}{4}\right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.565 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (2 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.287 |
|
|
\[ {}u^{\prime \prime }+\frac {u^{\prime }}{8}+4 u = 3 \cos \left (6 t \right ) \] |
1 |
1 |
1 |
kovacic, second_order_linear_constant_coeff |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
2.457 |
|
|
\[ {}u^{\prime \prime }+u^{\prime }+\frac {u^{3}}{5} = \cos \left (t \right ) \] |
1 |
0 |
0 |
unknown |
[NONE] |
❇ |
N/A |
0.103 |
|
|
\[ {}y^{\prime \prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
0.523 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.836 |
|
|
\[ {}y^{\prime \prime }+k^{2} x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.906 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
0.883 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.98 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.959 |
|
|
\[ {}\left (x^{2}+1\right ) y^{\prime \prime }-4 x y^{\prime }+6 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.736 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.764 |
|
|
\[ {}\left (-x^{2}+3\right ) y^{\prime \prime }-3 x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
0.93 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
0.961 |
|
|
\[ {}2 y^{\prime \prime }+x y^{\prime }+3 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.135 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.22 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.2 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.384 |
|
|
\[ {}y^{\prime \prime }-2 x y^{\prime }+\lambda y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.231 |
|
|
\[ {}y^{\prime \prime }-x y^{\prime }-y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.095 |
|
|
\[ {}\left (x^{2}+2\right ) y^{\prime \prime }-x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.167 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.152 |
|
|
\[ {}\left (-x^{2}+4\right ) y^{\prime \prime }+x y^{\prime }+2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.801 |
|
|
\[ {}y^{\prime \prime }+x^{2} y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
2.064 |
|
|
\[ {}\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-2 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
2.602 |
|
|
\[ {}y^{\prime \prime }+x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
2.16 |
|
|
\[ {}y^{\prime \prime }+y^{\prime } \sin \left (x \right )+\cos \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
3.104 |
|
|
\[ {}x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+3 y \ln \left (x \right ) = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.661 |
|
|
\[ {}y^{\prime \prime }+x^{2} y^{\prime }+\sin \left (x \right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
5.214 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.216 |
|
|
\[ {}y^{\prime \prime }+4 y^{\prime }+6 x y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.325 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.72 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.005 |
|
|
\[ {}\left (x^{2}-2 x -3\right ) y^{\prime \prime }+x y^{\prime }+4 y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.976 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.957 |
|
|
\[ {}\left (x^{3}+1\right ) y^{\prime \prime }+4 x y^{\prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
3.497 |
|
|
\[ {}x y^{\prime \prime }+y = 0 \] |
1 |
1 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.108 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+\alpha ^{2} y = 0 \] |
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)]‘]] |
✓ |
✓ |
1.509 |
|
|
\[ {}y^{\prime }-y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_quadrature] |
✓ |
✓ |
0.5 |
|
|
\[ {}y^{\prime }-x y = 0 \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.516 |
|
|
\[ {}\left (1-x \right ) y^{\prime } = y \] |
1 |
2 |
1 |
first order ode series method. Ordinary point, first order ode series method. Taylor series method |
[_separable] |
✓ |
✓ |
0.556 |
|
|
\[ {}\left (-x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+\alpha \left (\alpha +1\right ) y = 0 \] |
1 |
2 |
1 |
second order series method. Ordinary point, second order series method. Taylor series method |
[_Gegenbauer] |
✓ |
✓ |
1.694 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{10}+\frac {3 x_{2}}{40} \\ x_{2}^{\prime }=\frac {x_{1}}{10}-\frac {x_{2}}{5} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.543 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.727 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.682 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.857 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.785 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.781 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.048 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.487 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.594 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.626 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=\frac {3 x_{1}}{4}-2 x_{2} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{4} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.766 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {4 x_{1}}{5}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}+\frac {6 x_{2}}{5} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.747 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=-\frac {x_{3}}{4} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.807 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{4}+x_{2} \\ x_{2}^{\prime }=-x_{1}-\frac {x_{2}}{4} \\ x_{3}^{\prime }=\frac {x_{3}}{10} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.736 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.556 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.439 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {3 x_{1}}{2}+x_{2} \\ x_{2}^{\prime }=-\frac {x_{1}}{4}-\frac {x_{2}}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.582 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {5 x_{1}}{2}+2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-x_{2}+x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.964 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.536 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}+\frac {x_{2}}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.546 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+\frac {3 x_{2}}{2} \\ x_{2}^{\prime }=-\frac {3 x_{1}}{2}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.545 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+9 x_{2} \\ x_{2}^{\prime }=-x_{1}-3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.361 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-4 x_{1}+x_{2} \\ x_{3}^{\prime }=3 x_{1}+6 x_{2}+2 x_{3} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.74 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{2}+x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}-\frac {5 x_{2}}{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+x_{2}-\frac {5 x_{3}}{2} \end {array}\right ] \] |
1 |
1 |
3 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.677 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.206 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+\sqrt {3}\, x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=\sqrt {3}\, x_{1}-x_{2}+\sqrt {3}\, {\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.966 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}-\cos \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sin \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.969 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+{\mathrm e}^{-2 t} \\ x_{2}^{\prime }=4 x_{1}-2 x_{2}-2 \,{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.288 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}-2 x_{2}+\frac {1}{t^{3}} \\ x_{2}^{\prime }=8 x_{1}-4 x_{2}-\frac {1}{t^{2}} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.799 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}+2 x_{2}+\frac {1}{t} \\ x_{2}^{\prime }=2 x_{1}-x_{2}+\frac {2}{t}+4 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.916 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+2 \,{\mathrm e}^{t} \\ x_{2}^{\prime }=4 x_{1}+x_{2}-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.182 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}-{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.031 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {5 x_{1}}{4}+\frac {3 x_{2}}{4}+2 t \\ x_{2}^{\prime }=\frac {3 x_{1}}{4}-\frac {5 x_{2}}{4}+{\mathrm e}^{t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.267 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+\sqrt {2}\, x_{2}+{\mathrm e}^{-t} \\ x_{2}^{\prime }=\sqrt {2}\, x_{1}-2 x_{2}-{\mathrm e}^{-t} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.92 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\cos \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.759 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\csc \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\sec \left (t \right ) \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-\frac {x_{1}}{2}-\frac {x_{2}}{8}+\frac {{\mathrm e}^{-\frac {t}{2}}}{2} \\ x_{2}^{\prime }=2 x_{1}-\frac {x_{2}}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}+2 \,{\mathrm e}^{-t} \\ x_{2}^{\prime }=x_{1}-2 x_{2}+3 t \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.834 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.564 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}+x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.542 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{2} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.51 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}-7 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.547 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-2 x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.613 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.756 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-\frac {5 x_{2}}{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.495 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.529 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2} \\ x_{2}^{\prime }=-5 x_{1} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.307 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1} \\ x_{2}^{\prime }=-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.416 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-\frac {5 x_{2}}{2} \\ x_{2}^{\prime }=\frac {9 x_{1}}{5}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.791 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-x_{2} \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.484 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2}-2 \\ x_{2}^{\prime }=x_{1}-2 x_{2}+1 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.953 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-1 \\ x_{2}^{\prime }=2 x_{1}-x_{2}+5 \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.035 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=-2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.399 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.363 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-x \\ y^{\prime }=2 y \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.384 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.486 |
|
|
\[ {}\left [\begin {array}{c} x^{\prime }=-y \\ y^{\prime }=x \end {array}\right ] \] |
1 |
1 |
2 |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.469 |
|
|
|
|||||||||
|
|
|||||||||
|
|