|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=47 x_{1}-8 x_{2}+5 x_{3}-5 x_{4} \\ x_{2}^{\prime }=-10 x_{1}+32 x_{2}+18 x_{3}-2 x_{4} \\ x_{3}^{\prime }=139 x_{1}-40 x_{2}-167 x_{3}-121 x_{4} \\ x_{4}^{\prime }=-232 x_{1}+64 x_{2}+360 x_{3}+248 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.171 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.419 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.885 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-x_{2} \\ x_{3}^{\prime }=6 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.373 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.362 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.393 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=x_{4} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.532 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.366 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.360 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.409 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.470 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.660 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.349 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=25 x_{1}+12 x_{2} \\ x_{2}^{\prime }=-18 x_{1}-5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+13 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.505 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=-8 x_{1}+4 x_{2}+33 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.418 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.390 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.390 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.273 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.307 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.339 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{1}+3 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.516 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.360 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }=-27 x_{1}-9 x_{2}-5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.529 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}-4 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.376 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.408 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.370 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.302 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }=-x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}+3 x_{3} \\ x_{4}^{\prime }=-6 x_{2}-14 x_{3}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }=72 x_{1}+16 x_{2}-29 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.469 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }=-15 x_{1}-30 x_{2}-57 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.687 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.407 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.329 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=8 x_{1}-8 x_{2}+10 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.511 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }=17 x_{1}+7 x_{2}+5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.435 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.130 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }=-27 x_{2}+45 x_{3}-25 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.826 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.007 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }=3 x_{2} \\ x_{3}^{\prime }=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.190 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+x_{4} \\ x_{3}^{\prime }=3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=4 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.575 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }=-18 x_{1}-x_{2} \\ x_{3}^{\prime }=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.127 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.358 |
|
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.325 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.362 |
|
|
\[
{}2 x y+y^{\prime } = 0
\] |
[_separable] |
✓ |
0.416 |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
0.371 |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.632 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.411 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime } = y
\] |
[_separable] |
✓ |
0.891 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.633 |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.639 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.590 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.627 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.632 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.413 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.536 |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
0.524 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.090 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.106 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.633 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.650 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.693 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.687 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.891 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.493 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.623 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.644 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.532 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.655 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.599 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.589 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.651 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.667 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.756 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.544 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.599 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.532 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.605 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.514 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.486 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.610 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.539 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.538 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.684 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.720 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.697 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.637 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.745 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.629 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.634 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.589 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.759 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.935 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.708 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.641 |
|
|
\[
{}y^{\prime \prime } = x y
\] |
[[_Emden, _Fowler]] |
✓ |
0.522 |
|
|
\[
{}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.511 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.805 |
|
|
\[
{}y+y^{\prime } = 1+t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.929 |
|