|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x^{2} y^{\prime \prime }+\left (x +3\right ) x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.588 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.428 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.625 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (x^{2}-2 x \right ) y^{\prime }-\left (3 x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.238 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +4\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.218 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-v \left (v -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.631 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +1\right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.114 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x +1\right ) y^{\prime }+2 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.490 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.125 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a +2 b \right ) x^{2} y^{\prime }+\left (\left (a +b \right ) b \,x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.253 |
|
|
\[
{}x^{2} y^{\prime \prime }+a \,x^{2} y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.369 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 a x +b \right ) x y^{\prime }+\left (a b x +c \,x^{2}+d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.475 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.265 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{3} y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.536 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}+2\right ) x y^{\prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.351 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 x \left (x^{2}-a \right ) y^{\prime }+\left (2 n \,x^{2}+\left (\left (-1\right )^{n}-1\right ) a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.412 |
|
|
\[
{}x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (4 x^{4}+2 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.309 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2}+b \right ) x y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.776 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.791 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (-x^{4}+\left (2 n +2 a +1\right ) x^{2}+\left (-1\right )^{n} a -a^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.057 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{n}+b \right ) y^{\prime } x +\left (\operatorname {a1} \,x^{2 n}+\operatorname {b1} \,x^{n}+\operatorname {c1} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.839 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{\operatorname {a1}}+b \right ) x y^{\prime }+\left (A \,x^{2 \operatorname {a1}}+B \,x^{\operatorname {a1}}+C \,x^{\operatorname {b1}}+\operatorname {DD} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.010 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (2 x^{2} \tan \left (x \right )-x \right ) y^{\prime }-\left (x \tan \left (x \right )+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.394 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (2 x^{2} \cot \left (x \right )+x \right ) y^{\prime }+\left (x \cot \left (x \right )+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.573 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x f \left (x \right ) y^{\prime }+\left (f^{\prime }\left (x \right ) x +f \left (x \right )^{2}-f \left (x \right )+a \,x^{2}+b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.006 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} f \left (x \right ) y^{\prime }+\left (x^{2} \left (f^{\prime }\left (x \right )+f \left (x \right )^{2}+a \right )-v \left (v -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.013 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x -2 x^{2} f \left (x \right )\right ) y^{\prime }+\left (x^{2} \left (1+f \left (x \right )^{2}-f^{\prime }\left (x \right )\right )-f \left (x \right ) x -v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.988 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.572 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.502 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.332 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.888 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.954 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.197 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+3 y^{\prime } x +a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.204 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y-2 \cos \left (x \right )+2 x = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.684 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }+a x y^{\prime }+\left (a -2\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.727 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-v \left (v +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.525 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-n \left (n +1\right ) y+\frac {d}{d x}\operatorname {LegendreP}\left (n , x\right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.638 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +2 = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.392 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.956 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x +f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.706 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.079 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -a = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
2.057 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -l y = 0
\] |
[_Gegenbauer] |
✗ |
0.871 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
0.928 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 y^{\prime } x -\left (v +2\right ) \left (v -1\right ) y = 0
\] |
[_Gegenbauer] |
✗ |
630.059 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-\left (3 x +1\right ) y^{\prime }-\left (x^{2}-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.704 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+4 y^{\prime } x +\left (x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.766 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 \left (n +1\right ) x y^{\prime }-\left (v +n +1\right ) \left (v -n \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
1.275 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (n -1\right ) x y^{\prime }-\left (v -n +1\right ) \left (v +n \right ) y = 0
\] |
[_Gegenbauer] |
✗ |
1.274 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }-2 \left (v -1\right ) x y^{\prime }-2 v y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.763 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+2 a x y^{\prime }+a \left (a -1\right ) y = 0
\] |
[_Gegenbauer] |
✓ |
2.749 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{2}+c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.225 |
|
|
\[
{}\left (x^{2}-1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.234 |
|
|
\[
{}\left (-a^{2}+x^{2}\right ) y^{\prime \prime }+8 y^{\prime } x +12 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.181 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }-\left (x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.181 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.203 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (3 x +2\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.324 |
|
|
\[
{}\left (x^{2}+x -2\right ) y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }-\left (6 x^{2}+7 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.502 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+a y^{\prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.424 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }-v \left (v +1\right ) y = 0
\] |
[_Jacobi] |
✗ |
0.895 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime } = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.326 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[_Jacobi] |
✗ |
1.305 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (a +1\right ) x +b \right ) y^{\prime }-l y = 0
\] |
[_Jacobi] |
✗ |
1.319 |
|
|
\[
{}x \left (x -1\right ) y^{\prime \prime }+\left (\left (\operatorname {a1} +\operatorname {b1} +1\right ) x -\operatorname {d1} \right ) y^{\prime }+\operatorname {a1} \operatorname {b1} \operatorname {d1} = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
1.332 |
|
|
\[
{}x \left (x +2\right ) y^{\prime \prime }+2 \left (n +1+\left (n +1-2 l \right ) x -l \,x^{2}\right ) y^{\prime }+\left (2 l \left (p -n -1\right ) x +2 p l +m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.473 |
|
|
\[
{}\left (x +1\right )^{2} y^{\prime \prime }+\left (x^{2}+x -1\right ) y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.725 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y-\left (20 x +30\right ) \left (x^{2}+3 x \right )^{{7}/{3}} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.898 |
|
|
\[
{}\left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.655 |
|
|
\[
{}\left (x -1\right ) \left (x -2\right ) y^{\prime \prime }-\left (2 x -3\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
290.934 |
|
|
\[
{}\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.078 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-\left (2 x^{2}+l -5 x \right ) y^{\prime }-\left (4 x -1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.852 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y = 0
\] |
[_Jacobi] |
✗ |
0.700 |
|
|
\[
{}2 x \left (x -1\right ) y^{\prime \prime }+\left (\left (2 v +5\right ) x -2 v -3\right ) y^{\prime }+\left (v +1\right ) y = 0
\] |
[_Jacobi] |
✗ |
1.108 |
|
|
\[
{}\left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.419 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.747 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (4 a^{2} x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.924 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-\left (-4 k x +4 m^{2}+x^{2}-1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.602 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-v^{2}+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.796 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +\left (-x^{2}+2 \left (1-m +2 l \right ) x -m^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.872 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (4 x^{2}+1\right ) y-4 \sqrt {x^{3}}\, {\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.819 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x -\left (a \,x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.257 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 y^{\prime } x +f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.456 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+5 y^{\prime } x -y-\ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.943 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 y^{\prime } x -\left (4 x^{2}+12 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.385 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-4 x \left (2 x -1\right ) y^{\prime }+\left (4 x^{2}-4 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.972 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+6\right ) \left (x^{2}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.888 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+4 x^{2} \ln \left (x \right ) y^{\prime }+\left (x^{2} \ln \left (x \right )^{2}+2 x -8\right ) y-4 x^{2} \sqrt {{\mathrm e}^{x} x^{-x}} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.498 |
|
|
\[
{}\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }-12 y-3 x -1 = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.429 |
|
|
\[
{}x \left (4 x -1\right ) y^{\prime \prime }+\left (\left (4 a +2\right ) x -a \right ) y^{\prime }+a \left (a -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.176 |
|
|
\[
{}\left (3 x -1\right )^{2} y^{\prime \prime }+3 \left (3 x -1\right ) y^{\prime }-9 y-\ln \left (3 x -1\right )^{2} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.906 |
|
|
\[
{}9 x \left (x -1\right ) y^{\prime \prime }+3 \left (2 x -1\right ) y^{\prime }-20 y = 0
\] |
[_Jacobi] |
✓ |
1.425 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+\left (4 x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.308 |
|
|
\[
{}16 x^{2} y^{\prime \prime }+32 y^{\prime } x -\left (4 x +5\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.508 |
|
|
\[
{}\left (27 x^{2}+4\right ) y^{\prime \prime }+27 y^{\prime } x -3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.131 |
|
|
\[
{}48 x \left (x -1\right ) y^{\prime \prime }+\left (152 x -40\right ) y^{\prime }+53 y = 0
\] |
[_Jacobi] |
✗ |
1.283 |
|
|
\[
{}50 x \left (x -1\right ) y^{\prime \prime }+25 \left (2 x -1\right ) y^{\prime }-2 y = 0
\] |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
2.906 |
|
|
\[
{}144 x \left (x -1\right ) y^{\prime \prime }+\left (120 x -48\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✗ |
1.112 |
|
|
\[
{}144 x \left (x -1\right ) y^{\prime \prime }+\left (168 x -96\right ) y^{\prime }+y = 0
\] |
[_Jacobi] |
✗ |
0.934 |
|
|
\[
{}a \,x^{2} y^{\prime \prime }+b x y^{\prime }+\left (c \,x^{2}+d x +f \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.923 |
|