|
# |
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 |
✓ |
0.939 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=139 x_{1}-14 x_{2}-52 x_{3}-14 x_{4}+28 x_{5} \\ x_{2}^{\prime }=-22 x_{1}+5 x_{2}+7 x_{3}+8 x_{4}-7 x_{5} \\ x_{3}^{\prime }=370 x_{1}-38 x_{2}-139 x_{3}-38 x_{4}+76 x_{5} \\ x_{4}^{\prime }=152 x_{1}-16 x_{2}-59 x_{3}-13 x_{4}+35 x_{5} \\ x_{5}^{\prime }=95 x_{1}-10 x_{2}-38 x_{3}-7 x_{4}+23 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.497 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+13 x_{2}-13 x_{6} \\ x_{2}^{\prime }=-14 x_{1}+19 x_{2}-10 x_{3}-20 x_{4}+10 x_{5}+4 x_{6} \\ x_{3}^{\prime }=-30 x_{1}+12 x_{2}-7 x_{3}-30 x_{4}+12 x_{5}+18 x_{6} \\ x_{4}^{\prime }=-12 x_{1}+10 x_{2}-10 x_{3}-9 x_{4}+10 x_{5}+2 x_{6} \\ x_{5}^{\prime }=6 x_{1}+9 x_{2}+6 x_{4}+5 x_{5}-15 x_{6} \\ x_{6}^{\prime }=-14 x_{1}+23 x_{2}-10 x_{3}-20 x_{4}+10 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
2.770 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=9 x_{1}+4 x_{2} \\ x_{2}^{\prime }=-6 x_{1}-x_{2} \\ x_{3}^{\prime }=6 x_{1}+4 x_{2}+3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-3 x_{2} \\ x_{2}^{\prime }=3 x_{1}+7 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.410 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{2}+2 x_{3} \\ x_{2}^{\prime }=-5 x_{1}-3 x_{2}-7 x_{3} \\ x_{3}^{\prime }=x_{1} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.452 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=x_{4} \\ x_{3}^{\prime }=-2 x_{1}+2 x_{2}-3 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{1}-2 x_{2}+x_{3}-3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.569 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+x_{2} \\ x_{2}^{\prime }=-x_{1}-4 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.406 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.384 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-2 x_{2} \\ x_{2}^{\prime }=2 x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.415 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-x_{2} \\ x_{2}^{\prime }=x_{1}+5 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.389 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=7 x_{1}+x_{2} \\ x_{2}^{\prime }=-4 x_{1}+3 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.419 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2} \\ x_{2}^{\prime }=4 x_{1}+9 x_{2} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.402 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1} \\ x_{2}^{\prime }=-7 x_{1}+9 x_{2}+7 x_{3} \\ x_{3}^{\prime }=2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.322 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=25 x_{1}+12 x_{2} \\ x_{2}^{\prime }=-18 x_{1}-5 x_{2} \\ x_{3}^{\prime }=6 x_{1}+6 x_{2}+13 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.428 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-19 x_{1}+12 x_{2}+84 x_{3} \\ x_{2}^{\prime }=5 x_{2} \\ x_{3}^{\prime }=-8 x_{1}+4 x_{2}+33 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-13 x_{1}+40 x_{2}-48 x_{3} \\ x_{2}^{\prime }=-8 x_{1}+23 x_{2}-24 x_{3} \\ x_{3}^{\prime }=3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.439 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}-4 x_{3} \\ x_{2}^{\prime }=-x_{1}-x_{2}-x_{3} \\ x_{3}^{\prime }=x_{1}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.357 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=-x_{2}+x_{3} \\ x_{3}^{\prime }=x_{1}-x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.336 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{3} \\ x_{2}^{\prime }=x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}-3 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.345 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{3} \\ x_{2}^{\prime }=-5 x_{1}-x_{2}-5 x_{3} \\ x_{3}^{\prime }=4 x_{1}+x_{2}-2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}-9 x_{2} \\ x_{2}^{\prime }=x_{1}+4 x_{2} \\ x_{3}^{\prime }=x_{1}+3 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.352 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=-2 x_{1}-2 x_{2}-3 x_{3} \\ x_{3}^{\prime }=2 x_{1}+3 x_{2}+4 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.383 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=18 x_{1}+7 x_{2}+4 x_{3} \\ x_{3}^{\prime }=-27 x_{1}-9 x_{2}-5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.438 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1} \\ x_{2}^{\prime }=x_{1}+3 x_{2}+x_{3} \\ x_{3}^{\prime }=-2 x_{1}-4 x_{2}-x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.361 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}-4 x_{2}-2 x_{4} \\ x_{2}^{\prime }=x_{2} \\ x_{3}^{\prime }=6 x_{1}-12 x_{2}-x_{3}-6 x_{4} \\ x_{4}^{\prime }=-4 x_{2}-x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.489 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}+x_{4} \\ x_{2}^{\prime }=2 x_{2}+x_{3} \\ x_{3}^{\prime }=2 x_{3}+x_{4} \\ x_{4}^{\prime }=2 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.444 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}-4 x_{2} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=x_{1}+2 x_{2}+x_{3} \\ x_{4}^{\prime }=x_{2}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.427 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=x_{1}+3 x_{2}+7 x_{3} \\ x_{2}^{\prime }=-x_{2}-4 x_{3} \\ x_{3}^{\prime }=x_{2}+3 x_{3} \\ x_{4}^{\prime }=-6 x_{2}-14 x_{3}+x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.470 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=39 x_{1}+8 x_{2}-16 x_{3} \\ x_{2}^{\prime }=-36 x_{1}-5 x_{2}+16 x_{3} \\ x_{3}^{\prime }=72 x_{1}+16 x_{2}-29 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.473 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=28 x_{1}+50 x_{2}+100 x_{3} \\ x_{2}^{\prime }=15 x_{1}+33 x_{2}+60 x_{3} \\ x_{3}^{\prime }=-15 x_{1}-30 x_{2}-57 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.498 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-2 x_{1}+17 x_{2}+4 x_{3} \\ x_{2}^{\prime }=-x_{1}+6 x_{2}+x_{3} \\ x_{3}^{\prime }=x_{2}+2 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.433 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=5 x_{1}-x_{2}+x_{3} \\ x_{2}^{\prime }=x_{1}+3 x_{2} \\ x_{3}^{\prime }=-3 x_{1}+2 x_{2}+x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.425 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-3 x_{1}+5 x_{2}-5 x_{3} \\ x_{2}^{\prime }=3 x_{1}-x_{2}+3 x_{3} \\ x_{3}^{\prime }=8 x_{1}-8 x_{2}+10 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.436 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-15 x_{1}-7 x_{2}+4 x_{3} \\ x_{2}^{\prime }=34 x_{1}+16 x_{2}-11 x_{3} \\ x_{3}^{\prime }=17 x_{1}+7 x_{2}+5 x_{3} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.490 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=-x_{1}+x_{2}+x_{3}-2 x_{4} \\ x_{2}^{\prime }=7 x_{1}-4 x_{2}-6 x_{3}+11 x_{4} \\ x_{3}^{\prime }=5 x_{1}-x_{2}+x_{3}+3 x_{4} \\ x_{4}^{\prime }=6 x_{1}-2 x_{2}-2 x_{3}+6 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.779 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}+x_{2}-2 x_{3}+x_{4} \\ x_{2}^{\prime }=3 x_{2}-5 x_{3}+3 x_{4} \\ x_{3}^{\prime }=-13 x_{2}+22 x_{3}-12 x_{4} \\ x_{4}^{\prime }=-27 x_{2}+45 x_{3}-25 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.753 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=35 x_{1}-12 x_{2}+4 x_{3}+30 x_{4} \\ x_{2}^{\prime }=22 x_{1}-8 x_{2}+3 x_{3}+19 x_{4} \\ x_{3}^{\prime }=-10 x_{1}+3 x_{2}-9 x_{4} \\ x_{4}^{\prime }=-27 x_{1}+9 x_{2}-3 x_{3}-23 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.645 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=11 x_{1}-x_{2}+26 x_{3}+6 x_{4}-3 x_{5} \\ x_{2}^{\prime }=3 x_{2} \\ x_{3}^{\prime }=-9 x_{1}-24 x_{3}-6 x_{4}+3 x_{5} \\ x_{4}^{\prime }=3 x_{1}+9 x_{3}+5 x_{4}-x_{5} \\ x_{5}^{\prime }=-48 x_{1}-3 x_{2}-138 x_{3}-30 x_{4}+18 x_{5} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.964 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=3 x_{1}-4 x_{2}+x_{3} \\ x_{2}^{\prime }=4 x_{1}+3 x_{2}+x_{4} \\ x_{3}^{\prime }=3 x_{3}-4 x_{4} \\ x_{4}^{\prime }=4 x_{3}+3 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
0.557 |
|
|
\[
{}\left [\begin {array}{c} x_{1}^{\prime }=2 x_{1}-8 x_{3}-3 x_{4} \\ x_{2}^{\prime }=-18 x_{1}-x_{2} \\ x_{3}^{\prime }=-9 x_{1}-3 x_{2}-25 x_{3}-9 x_{4} \\ x_{4}^{\prime }=33 x_{1}+10 x_{2}+90 x_{3}+32 x_{4} \end {array}\right ]
\] |
system_of_ODEs |
✓ |
1.030 |
|
|
\[
{}y^{\prime } = y
\] |
[_quadrature] |
✓ |
0.333 |
|
|
\[
{}y^{\prime } = 4 y
\] |
[_quadrature] |
✓ |
0.565 |
|
|
\[
{}2 y^{\prime }+3 y = 0
\] |
[_quadrature] |
✓ |
0.577 |
|
|
\[
{}y^{\prime }+2 x y = 0
\] |
[_separable] |
✓ |
0.593 |
|
|
\[
{}y^{\prime } = x^{2} y
\] |
[_separable] |
✓ |
0.586 |
|
|
\[
{}\left (x -2\right ) y^{\prime }+y = 0
\] |
[_separable] |
✓ |
0.605 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.603 |
|
|
\[
{}2 \left (x +1\right ) y^{\prime } = y
\] |
[_separable] |
✓ |
0.614 |
|
|
\[
{}\left (x -1\right ) y^{\prime }+2 y = 0
\] |
[_separable] |
✓ |
0.612 |
|
|
\[
{}2 \left (x -1\right ) y^{\prime } = 3 y
\] |
[_separable] |
✓ |
0.616 |
|
|
\[
{}y^{\prime \prime } = y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.577 |
|
|
\[
{}y^{\prime \prime } = 4 y
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.601 |
|
|
\[
{}y^{\prime \prime }+9 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.597 |
|
|
\[
{}y^{\prime \prime }+y = x
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.411 |
|
|
\[
{}y^{\prime } x +y = 0
\] |
[_separable] |
✓ |
0.507 |
|
|
\[
{}2 y^{\prime } x = y
\] |
[_separable] |
✓ |
0.509 |
|
|
\[
{}x^{2} y^{\prime }+y = 0
\] |
[_separable] |
✗ |
0.089 |
|
|
\[
{}x^{3} y^{\prime } = 2 y
\] |
[_separable] |
✗ |
0.097 |
|
|
\[
{}y^{\prime \prime }+4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.635 |
|
|
\[
{}y^{\prime \prime }-4 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.625 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime }+y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.662 |
|
|
\[
{}y^{\prime \prime }+y^{\prime }-2 y = 0
\] |
[[_2nd_order, _missing_x]] |
✓ |
0.671 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}y^{\prime } = 1+y^{2}
\] |
[_quadrature] |
✓ |
1.461 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.592 |
|
|
\[
{}\left (x^{2}+2\right ) y^{\prime \prime }+4 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.594 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.496 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+6 y^{\prime } x +4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.586 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.534 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-6 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.543 |
|
|
\[
{}\left (x^{2}+3\right ) y^{\prime \prime }-7 y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.602 |
|
|
\[
{}\left (-x^{2}+2\right ) y^{\prime \prime }-y^{\prime } x +16 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.591 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[_Gegenbauer] |
✓ |
0.603 |
|
|
\[
{}3 y^{\prime \prime }+y^{\prime } x -4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.493 |
|
|
\[
{}5 y^{\prime \prime }-2 y^{\prime } x +10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }-x^{2} y^{\prime }-3 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.515 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.556 |
|
|
\[
{}y^{\prime \prime }+x y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.455 |
|
|
\[
{}y^{\prime \prime }+x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.453 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.527 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x -2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.482 |
|
|
\[
{}y^{\prime \prime }+\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.524 |
|
|
\[
{}\left (-x^{2}+2 x \right ) y^{\prime \prime }-6 \left (x -1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.639 |
|
|
\[
{}\left (x^{2}-6 x +10\right ) y^{\prime \prime }-4 \left (x -3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.568 |
|
|
\[
{}\left (4 x^{2}+16 x +17\right ) y^{\prime \prime } = 8 y
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.606 |
|
|
\[
{}\left (x^{2}+6 x \right ) y^{\prime \prime }+\left (3 x +9\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.611 |
|
|
\[
{}y^{\prime \prime }+\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.508 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x +2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.664 |
|
|
\[
{}y^{\prime \prime }+x^{2} y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.566 |
|
|
\[
{}\left (x^{3}+1\right ) y^{\prime \prime }+x^{4} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.576 |
|
|
\[
{}y^{\prime \prime }+y^{\prime } x +\left (2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.582 |
|
|
\[
{}y^{\prime \prime }+{\mathrm e}^{-x} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.671 |
|
|
\[
{}\cos \left (x \right ) y^{\prime \prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.808 |
|
|
\[
{}x y^{\prime \prime }+\sin \left (x \right ) y^{\prime }+x y = 0
\] |
[_Lienard] |
✓ |
1.558 |
|
|
\[
{}y^{\prime \prime }-2 y^{\prime } x +2 \alpha y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.596 |
|
|
\[
{}y^{\prime \prime } = x y
\] |
[[_Emden, _Fowler]] |
✓ |
0.455 |
|
|
\[
{}3 y+y^{\prime } = {\mathrm e}^{-2 t}+t
\] |
[[_linear, ‘class A‘]] |
✓ |
1.417 |
|
|
\[
{}-2 y+y^{\prime } = {\mathrm e}^{2 t} t^{2}
\] |
[[_linear, ‘class A‘]] |
✓ |
1.891 |
|
|
\[
{}y+y^{\prime } = 1+t \,{\mathrm e}^{-t}
\] |
[[_linear, ‘class A‘]] |
✓ |
2.006 |
|