|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}2 t y^{\prime \prime }+\left (t +1\right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.778 |
|
|
\[ {}2 t^{2} y^{\prime \prime }-t y^{\prime }+\left (t +1\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.907 |
|
|
\[ {}4 t y^{\prime \prime }+3 y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.882 |
|
|
\[ {}2 t^{2} y^{\prime \prime }+\left (t^{2}-t \right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.164 |
|
|
\[ {}t^{3} y^{\prime \prime }-t y^{\prime }-\left (t^{2}+\frac {5}{4}\right ) y = 0 \] |
second order series method. Irregular singular point |
[[_2nd_order, _with_linear_symmetries]] |
❇ |
N/A |
2.046 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+t \right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.828 |
|
|
\[ {}t y^{\prime \prime }-\left (t^{2}+2\right ) y^{\prime }+t y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Lienard] |
✓ |
✓ |
2.205 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (-t^{2}+3 t \right ) y^{\prime }-t y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
1.906 |
|
|
\[ {}t^{2} y^{\prime \prime }+t \left (t +1\right ) y^{\prime }-y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.859 |
|
|
\[ {}t y^{\prime \prime }-\left (4+t \right ) y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Laguerre] |
✓ |
✓ |
2.333 |
|
|
\[ {}t^{2} y^{\prime \prime }+\left (t^{2}-3 t \right ) y^{\prime }+3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.273 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }-\left (t +1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.022 |
|
|
\[ {}t y^{\prime \prime }+t y^{\prime }+2 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.438 |
|
|
\[ {}t y^{\prime \prime }+\left (-t^{2}+1\right ) y^{\prime }+4 t y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
2.269 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+y t^{2} = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Lienard] |
✓ |
✓ |
1.756 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-v^{2}\right ) y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[_Bessel] |
✓ |
✓ |
2.526 |
|
|
\[ {}t y^{\prime \prime }+\left (1-t \right ) y^{\prime }+\lambda y = 0 \] |
second order series method. Regular singular point. Repeated root |
[_Laguerre] |
✓ |
✓ |
2.667 |
|
|
\[ {}2 \sin \left (t \right ) y^{\prime \prime }+\left (1-t \right ) y^{\prime }-2 y = 0 \] |
second order series method. Regular singular point. Difference not integer |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
89.232 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t +1\right ) y = 0 \] |
second order series method. Regular singular point. Complex roots |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
4.225 |
|
|
\[ {}t y^{\prime \prime }+y^{\prime }-4 y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_Emden, _Fowler]] |
✓ |
✓ |
1.659 |
|
|
\[ {}t^{2} y^{\prime \prime }-t \left (t +1\right ) y^{\prime }+y = 0 \] |
second order series method. Regular singular point. Repeated root |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
1.703 |
|
|
\[ {}t^{2} y^{\prime \prime }+t y^{\prime }+\left (t^{2}-1\right ) y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[_Bessel] |
✓ |
✓ |
4.155 |
|
|
\[ {}t y^{\prime \prime }+3 y^{\prime }-3 y = 0 \] |
second order series method. Regular singular point. Difference is integer |
[[_Emden, _Fowler]] |
✓ |
✓ |
4.17 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=6 x_{1}-3 x_{2} \\ x_{2}^{\prime }=2 x_{1}+x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.577 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.983 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}-x_{2}+6 x_{3} \\ x_{2}^{\prime }=-10 x_{1}+4 x_{2}-12 x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}-x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.043 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-7 x_{1}+6 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.905 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}+3 x_{3}+6 x_{4} \\ x_{2}^{\prime }=3 x_{1}+6 x_{2}+9 x_{3}+18 x_{4} \\ x_{3}^{\prime }=5 x_{1}+10 x_{2}+15 x_{3}+30 x_{4} \\ x_{4}^{\prime }=7 x_{1}+14 x_{2}+21 x_{3}+42 x_{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.295 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=4 x_{1}+x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.558 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=-2 x_{1}+2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.553 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2}-x_{3} \\ x_{3}^{\prime }=3 x_{1}+3 x_{2}-x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.707 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}+10 x_{2}+2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.896 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-x_{2}-2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.775 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-3 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.901 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{2} \\ x_{2}^{\prime }=-x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.837 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-5 x_{2} \\ x_{2}^{\prime }=x_{1}-3 x_{2} \\ x_{3}^{\prime }=x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.045 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=3 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=2 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.143 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-x_{3} \\ x_{3}^{\prime }=-2 x_{1}-x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.194 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2} \\ x_{2}^{\prime }=5 x_{1}-3 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.64 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-2 x_{2} \\ x_{2}^{\prime }=4 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.652 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+2 x_{3} \\ x_{2}^{\prime }=x_{1}-x_{2} \\ x_{3}^{\prime }=-2 x_{1}-x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.155 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{2} \\ x_{2}^{\prime }=-2 x_{1} \\ x_{3}^{\prime }=-3 x_{4} \\ x_{4}^{\prime }=3 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.183 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.459 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \\ x_{2}^{\prime }=2 x_{2}-x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.698 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}-3 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.903 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-x_{3} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+4 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.668 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2} \\ x_{2}^{\prime }=-x_{2} \\ x_{3}^{\prime }=-2 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.471 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-x_{3} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3} \\ x_{4}^{\prime }=-x_{3}+2 x_{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.6 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+2 x_{3} \\ x_{2}^{\prime }=-x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}+x_{2}+3 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.634 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-4 x_{1}-4 x_{2} \\ x_{2}^{\prime }=10 x_{1}+9 x_{2}+x_{3} \\ x_{3}^{\prime }=-4 x_{1}-3 x_{2}+x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.067 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.681 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=3 x_{3} \\ x_{4}^{\prime }=2 x_{3}+3 x_{4} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
0.817 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3}+{\mathrm e}^{t} \cos \left (2 t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.177 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+{\mathrm e}^{c t} \\ x_{2}^{\prime }=2 x_{1}+x_{2}-2 x_{3} \\ x_{3}^{\prime }=3 x_{1}+2 x_{2}+x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.136 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=4 x_{1}+5 x_{2}+4 \,{\mathrm e}^{t} \cos \left (t \right ) \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.867 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}-x_{2}+{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.023 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-5 x_{2}+\sin \left (t \right ) \\ x_{2}^{\prime }=x_{1}-2 x_{2}+\tan \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
3.764 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+f_{1} \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+f_{2} \left (t \right ) \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.004 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{2} \\ x_{3}^{\prime }=x_{2}+3 x_{3}+{\mathrm e}^{2 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.121 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}-2 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{1}+x_{2}+3 x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.353 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=3 x_{1}-2 x_{2}+{\mathrm e}^{3 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.088 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-t^{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+2 t \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.409 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+2 x_{3}+\sin \left (t \right ) \\ x_{2}^{\prime }=-x_{1}+2 x_{2}+x_{3} \\ x_{3}^{\prime }=4 x_{1}-x_{2}-x_{3} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.861 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+2 x_{2}-3 x_{3}+{\mathrm e}^{t} \\ x_{2}^{\prime }=x_{1}+x_{2}+2 x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}+4 x_{3}-{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.233 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-x_{2}+1 \\ x_{2}^{\prime }=-4 x_{2}-x_{3}+t \\ x_{3}^{\prime }=5 x_{2}+{\mathrm e}^{t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
4.827 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+x_{2}-x_{3}+{\mathrm e}^{2 t} \\ x_{2}^{\prime }=2 x_{1}+3 x_{2}-4 x_{3}+2 \,{\mathrm e}^{2 t} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-4 x_{3}+{\mathrm e}^{2 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
2.149 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-x_{2}-x_{3}+{\mathrm e}^{3 t} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3}-{\mathrm e}^{3 t} \\ x_{3}^{\prime }=-3 x_{1}+x_{2}-x_{3}-{\mathrm e}^{3 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.863 |
|
|
\[ {}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}+2 x_{2}+4 x_{3}+2 \,{\mathrm e}^{8 t} \\ x_{2}^{\prime }=2 x_{1}+2 x_{3}+{\mathrm e}^{8 t} \\ x_{3}^{\prime }=4 x_{1}+2 x_{2}+3 x_{3}+2 \,{\mathrm e}^{8 t} \end {array}\right ] \] |
system of linear ODEs |
system of linear ODEs |
✓ |
✓ |
1.789 |
|
|
\[ {}x y+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.477 |
|
|
\[ {}x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime } = 0 \] |
exact, bernoulli, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
6.561 |
|
|
\[ {}1+y^{2}+\left (x^{2}+1\right ) y^{\prime } = 0 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.349 |
|
|
\[ {}y+x y^{\prime } = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.438 |
|
|
\[ {}y^{\prime } = 2 x y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.27 |
|
|
\[ {}x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime } = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
4.193 |
|
|
\[ {}\sqrt {-x^{2}+1}+\sqrt {1-y^{2}}\, y^{\prime } = 0 \] |
exact, separable, differentialType, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.84 |
|
|
\[ {}\left (1+x \right ) y^{\prime }-1+y = 0 \] |
exact, linear, separable, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.157 |
|
|
\[ {}y^{\prime } \tan \left (x \right )-y = 1 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.954 |
|
|
\[ {}y+3+\cot \left (x \right ) y^{\prime } = 0 \] |
exact, linear, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.181 |
|
|
\[ {}y^{\prime } = \frac {x}{y} \] |
exact, separable, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.742 |
|
|
\[ {}x^{\prime } = 1-\sin \left (2 t \right ) \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.64 |
|
|
\[ {}y+x y^{\prime } = y^{2} \] |
exact, riccati, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.193 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.836 |
|
|
\[ {}\sec \left (x \right ) \cos \left (y\right )^{2} = \cos \left (x \right ) \sin \left (y\right ) y^{\prime } \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
11.779 |
|
|
\[ {}y+x y^{\prime } = x y \left (y^{\prime }-1\right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.763 |
|
|
\[ {}x y+\sqrt {x^{2}+1}\, y^{\prime } = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.79 |
|
|
\[ {}y = x y+x^{2} y^{\prime } \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.965 |
|
|
\[ {}\tan \left (x \right ) \sin \left (x \right )^{2}+\cos \left (x \right )^{2} \cot \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
21.288 |
|
|
\[ {}y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1 = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.517 |
|
|
\[ {}y^{\prime } = \frac {y}{x} \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.68 |
|
|
\[ {}x y^{\prime }+2 y = 0 \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
2.239 |
|
|
\[ {}\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime } = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.179 |
|
|
\[ {}x^{2} y^{\prime }+y^{2} = 0 \] |
exact, riccati, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.876 |
|
|
\[ {}y^{\prime } = {\mathrm e}^{y} \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.481 |
|
|
\[ {}{\mathrm e}^{y} \left (y^{\prime }+1\right ) = 1 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
1.162 |
|
|
\[ {}1+y^{2} = \frac {y^{\prime }}{x^{3} \left (-1+x \right )} \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
3.212 |
|
|
\[ {}x^{2}+3 x y^{\prime } = y^{3}+2 y \] |
abelFirstKind |
[_rational, _Abel] |
✗ |
N/A |
2.028 |
|
|
\[ {}\left (x^{2}+x +1\right ) y^{\prime } = y^{2}+2 y+5 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
22.352 |
|
|
\[ {}\left (x^{2}-2 x -8\right ) y^{\prime } = y^{2}+y-2 \] |
exact, riccati, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
8.253 |
|
|
\[ {}x +y = x y^{\prime } \] |
linear, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_linear] |
✓ |
✓ |
1.223 |
|
|
|
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