|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\frac {3 t^{2}}{y}-\frac {t^{3} y^{\prime }}{y^{2}} = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.835 |
|
|
\[ {}2 t +y^{3}+\left (3 t y^{2}+4\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational] |
✓ |
✓ |
1.446 |
|
|
\[ {}-\frac {1}{y}+\left (\frac {t}{y^{2}}+3 y^{2}\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
1.446 |
|
|
\[ {}2 t y+\left (t^{2}+y^{2}\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
10.187 |
|
|
\[ {}2 t y^{3}+\left (1+3 t^{2} y^{2}\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
3.243 |
|
|
\[ {}\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.826 |
|
|
\[ {}3 t^{2}+3 y^{2}+6 t y y^{\prime } = 0 \] |
exact, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
2.386 |
|
|
\[ {}{\mathrm e}^{t} \sin \left (y\right )+\left (1+{\mathrm e}^{t} \cos \left (y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
2.067 |
|
|
\[ {}3 t^{2} y+3 y^{2}-1+\left (t^{3}+6 t y\right ) y^{\prime } = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.608 |
|
|
\[ {}-2 t y^{2} \sin \left (t^{2}\right )+2 y \cos \left (t^{2}\right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.513 |
|
|
\[ {}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
11.457 |
|
|
\[ {}1-y^{2} \cos \left (t y\right )+\left (t y \cos \left (t y\right )+\sin \left (t y\right )\right ) y^{\prime } = 0 \] |
unknown |
[‘y=_G(x,y’)‘] |
❇ |
N/A |
8.605 |
|
|
\[ {}2 t \sin \left (y\right )-2 t y \sin \left (t^{2}\right )+\left (t^{2} \cos \left (y\right )+\cos \left (t^{2}\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
35.254 |
|
|
\[ {}\left (3+t \right ) \cos \left (t +y\right )+\sin \left (t +y\right )+\left (3+t \right ) \cos \left (t +y\right ) y^{\prime } = 0 \] |
exact, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
10.316 |
|
|
\[ {}\frac {2 t^{2} y \cos \left (t^{2}\right )-y \sin \left (t^{2}\right )}{t^{2}}+\frac {\left (2 t y+\sin \left (t^{2}\right )\right ) y^{\prime }}{t} = 0 \] |
exact |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
9.75 |
|
|
\[ {}-\frac {y^{2} {\mathrm e}^{\frac {y}{t}}}{t^{2}}+1+{\mathrm e}^{\frac {y}{t}} \left (1+\frac {y}{t}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.293 |
|
|
\[ {}2 t \sin \left (\frac {y}{t}\right )-y \cos \left (\frac {y}{t}\right )+t \cos \left (\frac {y}{t}\right ) y^{\prime } = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
3.123 |
|
|
\[ {}2 t y^{2}+2 t^{2} y y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.845 |
|
|
\[ {}1+\frac {y}{t^{2}}-\frac {y^{\prime }}{t} = 0 \] |
exact, linear, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.148 |
|
|
\[ {}2 t y+3 t^{2}+\left (t^{2}-1\right ) y^{\prime } = 0 \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.512 |
|
|
\[ {}1+5 t -y-\left (t +2 y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
5.456 |
|
|
\[ {}{\mathrm e}^{y}-2 t y+\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
❇ |
N/A |
4.658 |
|
|
\[ {}2 t y \,{\mathrm e}^{t^{2}}+2 t \,{\mathrm e}^{-y}+\left ({\mathrm e}^{t^{2}}-t^{2} {\mathrm e}^{-y}+1\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
36.807 |
|
|
\[ {}y^{2}-2 \sin \left (2 t \right )+\left (1+2 t y\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
8.174 |
|
|
\[ {}\cos \left (t \right )^{2}-\sin \left (t \right )^{2}+y+\left (\sec \left (y\right ) \tan \left (y\right )+t \right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
39.358 |
|
|
\[ {}\frac {1}{t^{2}+1}-y^{2}-2 t y y^{\prime } = 0 \] |
exact, bernoulli, first_order_ode_lie_symmetry_lookup |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
1.777 |
|
|
\[ {}\frac {2 t}{t^{2}+1}+y+\left ({\mathrm e}^{y}+t \right ) y^{\prime } = 0 \] |
exact |
[_exact] |
❇ |
N/A |
9.528 |
|
|
\[ {}-2 x -y \cos \left (x y\right )+\left (2 y-x \cos \left (x y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
35.291 |
|
|
\[ {}-4 x^{3}+6 y \sin \left (6 x y\right )+\left (4 y^{3}+6 x \sin \left (6 x y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
44.442 |
|
|
\[ {}t^{2} y+t^{3} y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.45 |
|
|
\[ {}y \left (2 \,{\mathrm e}^{t}+4 t \right )+3 \left ({\mathrm e}^{t}+t^{2}\right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.579 |
|
|
\[ {}y+\left (2 t -y \,{\mathrm e}^{y}\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
1.392 |
|
|
\[ {}2 t y+y^{2}-t^{2} y^{\prime } = 0 \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.324 |
|
|
\[ {}y+2 t^{2}+\left (t^{2} y-t \right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.399 |
|
|
\[ {}5 t y+4 y^{2}+1+\left (t^{2}+2 t y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.58 |
|
|
\[ {}5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime } = 0 \] |
riccati, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.608 |
|
|
\[ {}2 t +\tan \left (y\right )+\left (t -t^{2} \tan \left (y\right )\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
2.592 |
|
|
\[ {}2 t -y^{2} \sin \left (t y\right )+\left (\cos \left (t y\right )-t y \sin \left (t y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
11.434 |
|
|
\[ {}-1+{\mathrm e}^{t y} y+y \cos \left (t y\right )+\left (1+{\mathrm e}^{t y} t +t \cos \left (t y\right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
41.909 |
|
|
\[ {}2 t +2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.211 |
|
|
\[ {}\frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.082 |
|
|
\[ {}2 t +\frac {19 y}{10}+\left (\frac {19 t}{10}+2 y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.076 |
|
|
\[ {}y^{\prime }-\frac {y}{2} = \frac {t}{y} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
1.296 |
|
|
\[ {}y^{\prime }+y = t y^{2} \] |
riccati, bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
0.944 |
|
|
\[ {}2 t y^{\prime }-y = 2 t y^{3} \cos \left (t \right ) \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
35.666 |
|
|
\[ {}t y^{\prime }-y = t y^{3} \sin \left (t \right ) \] |
bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
32.289 |
|
|
\[ {}y^{\prime }-2 y = \frac {\cos \left (t \right )}{\sqrt {y}} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
10.556 |
|
|
\[ {}y^{\prime }+3 y = \sqrt {y}\, \sin \left (t \right ) \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
41.946 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t y^{2} \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.211 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t^{2}} \] |
riccati, bernoulli, exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.177 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = \frac {y^{2}}{t} \] |
exact, riccati, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.685 |
|
|
\[ {}y^{\prime }-\frac {y}{t} = t^{2} y^{\frac {3}{2}} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
2.291 |
|
|
\[ {}\cos \left (\frac {t}{t +y}\right )+{\mathrm e}^{\frac {2 y}{t}} y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.639 |
|
|
\[ {}y \ln \left (\frac {t}{y}\right )+\frac {t^{2} y^{\prime }}{t +y} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
15.695 |
|
|
\[ {}2 \ln \left (t \right )-\ln \left (4 y^{2}\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.747 |
|
|
\[ {}\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}} = 0 \] |
riccati, bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.791 |
|
|
\[ {}\frac {\sin \left (2 t \right )}{\cos \left (2 y\right )}+\frac {\ln \left (y\right ) y^{\prime }}{\ln \left (t \right )} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
30.221 |
|
|
\[ {}\sqrt {t^{2}+1}+y y^{\prime } = 0 \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.096 |
|
|
\[ {}2 t +\left (y-3 t \right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
3.185 |
|
|
\[ {}2 y-3 t +t y^{\prime } = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.466 |
|
|
\[ {}t y-y^{2}+t \left (t -3 y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.457 |
|
|
\[ {}t^{2}+t y+y^{2}-t y y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.678 |
|
|
\[ {}t^{3}+y^{3}-t y^{2} y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.089 |
|
|
\[ {}y^{\prime } = \frac {t +4 y}{4 t +y} \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.911 |
|
|
\[ {}t -y+t y^{\prime } = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
0.949 |
|
|
\[ {}y+\left (t +y\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.825 |
|
|
\[ {}2 t^{2}-7 t y+5 y^{2}+t y y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
15.009 |
|
|
\[ {}y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.359 |
|
|
\[ {}y^{2} = \left (t y-4 t^{2}\right ) y^{\prime } \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.947 |
|
|
\[ {}y-\left (3 \sqrt {t y}+t \right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.876 |
|
|
\[ {}\left (t^{2}-y^{2}\right ) y^{\prime }+y^{2}+t y = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.86 |
|
|
\[ {}t y y^{\prime }-t^{2} {\mathrm e}^{-\frac {y}{t}}-y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.488 |
|
|
\[ {}y^{\prime } = \frac {1}{\frac {2 y \,{\mathrm e}^{-\frac {t}{y}}}{t}+\frac {t}{y}} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.719 |
|
|
\[ {}t \left (\ln \left (t \right )-\ln \left (y\right )\right ) y^{\prime } = y \] |
exactByInspection, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
3.945 |
|
|
\[ {}y^{\prime }+2 y = t^{2} \sqrt {y} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
2.97 |
|
|
\[ {}y^{\prime }-2 y = t^{2} \sqrt {y} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✓ |
3.215 |
|
|
\[ {}y^{\prime } = \frac {4 y^{2}-t^{2}}{2 t y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.464 |
|
|
\[ {}t +y-t y^{\prime } = 0 \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.295 |
|
|
\[ {}t y^{\prime }-y-\sqrt {t^{2}+y^{2}} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
3.808 |
|
|
\[ {}t^{3}+y^{2} \sqrt {t^{2}+y^{2}}-t y \sqrt {t^{2}+y^{2}}\, y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
5.021 |
|
|
\[ {}y^{3}-t^{3}-t y^{2} y^{\prime } = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.701 |
|
|
\[ {}t y^{3}-\left (t^{4}+y^{4}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
6.012 |
|
|
\[ {}y^{4}+\left (t^{4}-t y^{3}\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
8.887 |
|
|
\[ {}t -2 y+1+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.077 |
|
|
\[ {}5 t +2 y+1+\left (2 t +y+1\right ) y^{\prime } = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.359 |
|
|
\[ {}3 t -y+1-\left (6 t -2 y-3\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.536 |
|
|
\[ {}2 t +3 y+1+\left (4 t +6 y+1\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.532 |
|
|
\[ {}y^{\prime }-\frac {2 y}{x} = -x^{2} y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.704 |
|
|
\[ {}y^{\prime }+y \cot \left (x \right ) = y^{4} \] |
bernoulli, first_order_ode_lie_symmetry_lookup |
[_Bernoulli] |
✓ |
✗ |
37.984 |
|
|
\[ {}t y^{\prime }-{y^{\prime }}^{3} = y \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.749 |
|
|
\[ {}t y^{\prime }-y-2 \left (t y^{\prime }-y\right )^{2} = y^{\prime }+1 \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
1.021 |
|
|
\[ {}t y^{\prime }-y-1 = {y^{\prime }}^{2}-y^{\prime } \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
0.456 |
|
|
\[ {}1+y-t y^{\prime } = \ln \left (y^{\prime }\right ) \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.332 |
|
|
\[ {}1-2 t y^{\prime }+2 y = \frac {1}{{y^{\prime }}^{2}} \] |
clairaut |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
1.589 |
|
|
\[ {}y = -t y^{\prime }+\frac {{y^{\prime }}^{5}}{5} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
0.66 |
|
|
\[ {}y = t {y^{\prime }}^{2}+3 {y^{\prime }}^{2}-2 {y^{\prime }}^{3} \] |
dAlembert |
[_dAlembert] |
✓ |
✓ |
59.272 |
|
|
\[ {}y = t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \] |
linear, homogeneousTypeMapleC, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.308 |
|
|
\[ {}y = t \left (2-y^{\prime }\right )+2 {y^{\prime }}^{2}+1 \] |
dAlembert |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
0.661 |
|
|
\[ {}t^{\frac {1}{3}} y^{\frac {2}{3}}+t +\left (t^{\frac {2}{3}} y^{\frac {1}{3}}+y\right ) y^{\prime } = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
5.841 |
|
|
\[ {}y^{\prime } = \frac {y^{2}-t^{2}}{t y} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
1.677 |
|
|
|
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