|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}-6 y_{3} \\ y_{2}^{\prime }=2 y_{1}+6 y_{2}+2 y_{3} \\ y_{3}^{\prime }=-2 y_{1}-2 y_{2}+2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.086 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+7 y_{2}-2 y_{3} \\ y_{3}^{\prime }=-10 y_{1}+10 y_{2}-5 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.992 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+5 y_{2}+y_{3} \\ y_{3}^{\prime }=-6 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.001 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}+7 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.608 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{2} \\ y_{2}^{\prime }=y_{1}-2 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.573 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-y_{1}-11 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.655 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=3 y_{1}+y_{2} \\ y_{2}^{\prime }=-y_{1}+y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.57 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}+12 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-8 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.646 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-10 y_{1}+9 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+2 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.659 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-13 y_{1}+16 y_{2} \\ y_{2}^{\prime }=-9 y_{1}+11 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.642 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}+y_{3} \\ y_{2}^{\prime }=-4 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=4 y_{2}+2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.056 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=\frac {y_{1}}{3}+\frac {y_{2}}{3}-y_{3} \\ y_{2}^{\prime }=-\frac {4 y_{1}}{3}-\frac {4 y_{2}}{3}+y_{3} \\ y_{3}^{\prime }=-\frac {2 y_{1}}{3}+\frac {y_{2}}{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.084 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{3} \\ y_{3}^{\prime }=-y_{1}+3 y_{2}-y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.994 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-2 y_{1}+3 y_{2}-y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.005 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=6 y_{1}-5 y_{2}+3 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}+y_{2}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.015 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+8 y_{2} \\ y_{2}^{\prime }=-2 y_{1}-3 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.625 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=15 y_{1}-9 y_{2} \\ y_{2}^{\prime }=16 y_{1}-9 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.637 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-4 y_{2} \\ y_{2}^{\prime }=y_{1}-7 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.607 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+24 y_{2} \\ y_{2}^{\prime }=-6 y_{1}+17 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.587 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}+3 y_{2} \\ y_{2}^{\prime }=-3 y_{1}-y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.558 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2}-2 y_{3} \\ y_{3}^{\prime }=-y_{1}-y_{2}-y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.085 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{2}^{\prime }=-2 y_{1}+2 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}+3 y_{2}+2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.724 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-7 y_{1}-4 y_{2}+4 y_{3} \\ y_{2}^{\prime }=y_{1}+y_{3} \\ y_{3}^{\prime }=-9 y_{1}-5 y_{2}+6 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.47 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-4 y_{2}-y_{3} \\ y_{2}^{\prime }=3 y_{1}+6 y_{2}+y_{3} \\ y_{3}^{\prime }=-3 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.972 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=4 y_{1}-8 y_{2}-4 y_{3} \\ y_{2}^{\prime }=-3 y_{1}-y_{2}-4 y_{3} \\ y_{3}^{\prime }=y_{1}-y_{2}+9 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.193 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-5 y_{1}-y_{2}+11 y_{3} \\ y_{2}^{\prime }=-7 y_{1}+y_{2}+13 y_{3} \\ y_{3}^{\prime }=-4 y_{1}+8 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.786 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-y_{2}+y_{3} \\ y_{2}^{\prime }=-y_{1}+9 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-2 y_{1}+2 y_{2}+4 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.747 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+10 y_{2}-12 y_{3} \\ y_{2}^{\prime }=2 y_{1}+2 y_{2}+3 y_{3} \\ y_{3}^{\prime }=2 y_{1}-y_{2}+6 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.734 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-6 y_{1}-4 y_{2}-4 y_{3} \\ y_{2}^{\prime }=2 y_{1}-y_{2}+y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{2}-2 y_{3} \\ y_{2}^{\prime }=-y_{1}+5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=y_{1}+y_{2}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.686 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-2 y_{1}-12 y_{2}+10 y_{3} \\ y_{2}^{\prime }=2 y_{1}-24 y_{2}+11 y_{3} \\ y_{3}^{\prime }=2 y_{1}-24 y_{2}+8 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.866 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}-12 y_{2}+8 y_{3} \\ y_{2}^{\prime }=y_{1}-9 y_{2}+4 y_{3} \\ y_{3}^{\prime }=y_{1}-6 y_{2}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.72 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-4 y_{1}-y_{3} \\ y_{2}^{\prime }=-y_{1}-3 y_{2}-y_{3} \\ y_{3}^{\prime }=y_{1}-2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.576 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+4 y_{3} \\ y_{2}^{\prime }=4 y_{1}+5 y_{2}-8 y_{3} \\ y_{3}^{\prime }=2 y_{1}+3 y_{2}-5 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.721 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-y_{2} \\ y_{2}^{\prime }=y_{1}-y_{2} \\ y_{3}^{\prime }=-y_{1}-y_{2}-2 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.562 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-y_{1}+2 y_{2} \\ y_{2}^{\prime }=-5 y_{1}+5 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.893 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-11 y_{1}+4 y_{2} \\ y_{2}^{\prime }=-26 y_{1}+9 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.877 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=y_{1}+2 y_{2} \\ y_{2}^{\prime }=-4 y_{1}+5 y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.882 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=5 y_{1}-6 y_{2} \\ y_{2}^{\prime }=3 y_{1}-y_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.83 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}-3 y_{2}+y_{3} \\ y_{2}^{\prime }=2 y_{2}+2 y_{3} \\ y_{3}^{\prime }=5 y_{1}+y_{2}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
23.811 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+3 y_{2}+y_{3} \\ y_{2}^{\prime }=y_{1}-5 y_{2}-3 y_{3} \\ y_{3}^{\prime }=-3 y_{1}+7 y_{2}+3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.683 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=2 y_{1}+y_{2}-y_{3} \\ y_{2}^{\prime }=y_{2}+y_{3} \\ y_{3}^{\prime }=y_{1}+y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.149 |
|
|
\[ {}\left [\begin {array}{c} y_{1}^{\prime }=-3 y_{1}+y_{2}-3 y_{3} \\ y_{2}^{\prime }=4 y_{1}-y_{2}+2 y_{3} \\ y_{3}^{\prime }=4 y_{1}-2 y_{2}+3 y_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.914 |
|
|
\[ {}y^{\prime }+\sin \left (t \right ) y = 0 \] |
linear |
[_separable] |
✓ |
✓ |
0.625 |
|
|
\[ {}y^{\prime }+{\mathrm e}^{t^{2}} y = 0 \] |
linear |
[_separable] |
✓ |
✓ |
1.033 |
|
|
\[ {}y^{\prime }-2 t y = t \] |
linear |
[_separable] |
✓ |
✓ |
0.301 |
|
|
\[ {}y^{\prime }+2 t y = t \] |
linear |
[_separable] |
✓ |
✓ |
0.571 |
|
|
\[ {}y^{\prime }+y = \frac {1}{t^{2}+1} \] |
linear |
[_linear] |
✓ |
✓ |
1.154 |
|
|
\[ {}\cos \left (t \right ) y+y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.659 |
|
|
\[ {}\sqrt {t}\, \sin \left (t \right ) y+y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.694 |
|
|
\[ {}\frac {2 t y}{t^{2}+1}+y^{\prime } = \frac {1}{t^{2}+1} \] |
exact, linear, differentialType, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.358 |
|
|
\[ {}y^{\prime }+y = t \,{\mathrm e}^{t} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_linear, ‘class A‘]] |
✓ |
✓ |
1.158 |
|
|
\[ {}y t^{2}+y^{\prime } = 1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.704 |
|
|
\[ {}y t^{2}+y^{\prime } = t^{2} \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.554 |
|
|
\[ {}\frac {t y}{t^{2}+1}+y^{\prime } = 1-\frac {t^{3} y}{t^{4}+1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.548 |
|
|
\[ {}\sqrt {t^{2}+1}\, y+y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.88 |
|
|
\[ {}\sqrt {t^{2}+1}\, y \,{\mathrm e}^{-t}+y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.794 |
|
|
\[ {}y^{\prime }-2 t y = t \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.138 |
|
|
\[ {}t y+y^{\prime } = t +1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
2.361 |
|
|
\[ {}y^{\prime }+y = \frac {1}{t^{2}+1} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
4.212 |
|
|
\[ {}y^{\prime }-2 t y = 1 \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.676 |
|
|
\[ {}t y+\left (t^{2}+1\right ) y^{\prime } = \left (t^{2}+1\right )^{\frac {5}{2}} \] |
linear, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.741 |
|
|
\[ {}4 t y+\left (t^{2}+1\right ) y^{\prime } = t \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.663 |
|
|
\[ {}y^{\prime }+\frac {y}{t} = \frac {1}{t^{2}} \] |
linear |
[_linear] |
✓ |
✓ |
0.322 |
|
|
\[ {}y^{\prime }+\frac {y}{\sqrt {t}} = {\mathrm e}^{\frac {\sqrt {t}}{2}} \] |
linear |
[_linear] |
✓ |
✓ |
0.467 |
|
|
\[ {}y^{\prime }+\frac {y}{t} = \cos \left (t \right )+\frac {\sin \left (t \right )}{t} \] |
linear |
[_linear] |
✓ |
✓ |
0.379 |
|
|
\[ {}y^{\prime }+\tan \left (t \right ) y = \cos \left (t \right ) \sin \left (t \right ) \] |
linear |
[_linear] |
✓ |
✓ |
0.446 |
|
|
\[ {}\left (t^{2}+1\right ) y^{\prime } = 1+y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.366 |
|
|
\[ {}y^{\prime } = \left (t +1\right ) \left (1+y\right ) \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.266 |
|
|
\[ {}y^{\prime } = 1-t +y^{2}-t y^{2} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.581 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{3+t +y} \] |
exact, separable, first order special form ID 1, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.211 |
|
|
\[ {}\cos \left (y\right ) \sin \left (t \right ) y^{\prime } = \cos \left (t \right ) \sin \left (y\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
35.884 |
|
|
\[ {}t^{2} \left (1+y^{2}\right )+2 y y^{\prime } = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.361 |
|
|
\[ {}y^{\prime } = \frac {2 t}{y+y t^{2}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.757 |
|
|
\[ {}\sqrt {t^{2}+1}\, y^{\prime } = \frac {t y^{3}}{\sqrt {t^{2}+1}} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.577 |
|
|
\[ {}y^{\prime } = \frac {3 t^{2}+4 t +2}{-2+2 y} \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.778 |
|
|
\[ {}\cos \left (y\right ) y^{\prime } = -\frac {t \sin \left (y\right )}{t^{2}+1} \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.118 |
|
|
\[ {}y^{\prime } = k \left (a -y\right ) \left (b -y\right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
2.215 |
|
|
\[ {}3 t y^{\prime } = \cos \left (t \right ) y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.656 |
|
|
\[ {}t y^{\prime } = y+\sqrt {t^{2}+y^{2}} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.692 |
|
|
\[ {}2 t y y^{\prime } = 3 y^{2}-t^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
2.518 |
|
|
\[ {}\left (t -\sqrt {t y}\right ) y^{\prime } = y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
4.657 |
|
|
\[ {}y^{\prime } = \frac {t +y}{t -y} \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.089 |
|
|
\[ {}{\mathrm e}^{\frac {t}{y}} \left (-t +y\right ) y^{\prime }+y \left (1+{\mathrm e}^{\frac {t}{y}}\right ) = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.985 |
|
|
\[ {}y^{\prime } = \frac {t +y+1}{t -y+3} \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.988 |
|
|
\[ {}1+t -2 y+\left (4 t -3 y-6\right ) y^{\prime } = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.902 |
|
|
\[ {}t +2 y+3+\left (2 t +4 y-1\right ) y^{\prime } = 0 \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.261 |
|
|
\[ {}2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
5.098 |
|
|
\[ {}1+{\mathrm e}^{t y} \left (1+t y\right )+\left (1+{\mathrm e}^{t y} t^{2}\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
2.973 |
|
|
\[ {}\sec \left (t \right ) \tan \left (t \right )+\sec \left (t \right )^{2} y+\left (\tan \left (t \right )+2 y\right ) y^{\prime } = 0 \] |
exact |
[_exact, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
24.539 |
|
|
\[ {}\frac {y^{2}}{2}-2 y \,{\mathrm e}^{t}+\left (-{\mathrm e}^{t}+y\right ) y^{\prime } = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_1st_order, _with_linear_symmetries], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.016 |
|
|
\[ {}2 t y^{3}+3 t^{2} y^{2} y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.492 |
|
|
\[ {}2 t \cos \left (y\right )+3 y t^{2}+\left (t^{3}-t^{2} \sin \left (y\right )-y\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
3.773 |
|
|
\[ {}3 t^{2}+4 t y+\left (2 t^{2}+2 y\right ) y^{\prime } = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
4.358 |
|
|
\[ {}2 t -2 \,{\mathrm e}^{t y} \sin \left (2 t \right )+{\mathrm e}^{t y} \cos \left (2 t \right ) y+\left (-3+{\mathrm e}^{t y} t \cos \left (2 t \right )\right ) y^{\prime } = 0 \] |
exact |
[_exact] |
✓ |
✓ |
9.996 |
|
|
\[ {}3 t y+y^{2}+\left (t^{2}+t y\right ) y^{\prime } = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
7.145 |
|
|
\[ {}y^{\prime } = y^{2}+\cos \left (t^{2}\right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
3.483 |
|
|
\[ {}y^{\prime } = 1+y+y^{2} \cos \left (t \right ) \] |
riccati |
[_Riccati] |
✓ |
✓ |
26.26 |
|
|
\[ {}y^{\prime } = t +y^{2} \] |
riccati |
[[_Riccati, _special]] |
✓ |
✓ |
1.521 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{-t^{2}}+y^{2} \] |
riccati |
[_Riccati] |
✓ |
✓ |
1.73 |
|
|
|
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