|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}x y^{\prime \prime }-y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.852 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }-y a \,x^{3} = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.658 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.512 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }-x y-{\mathrm e}^{x} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.942 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+y a x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
72.551 |
|
|
\[
{}x y^{\prime \prime }+2 y^{\prime }+a \,x^{2} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.856 |
|
|
\[
{}x y^{\prime \prime }-2 y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.887 |
|
|
\[
{}x y^{\prime \prime }+v y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.001 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.155 |
|
|
\[
{}x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.194 |
|
|
\[
{}x y^{\prime \prime }+\left (x +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.932 |
|
|
\[
{}x y^{\prime \prime }+\left (x +a +b \right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.039 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x -y-x \left (x +1\right ) {\mathrm e}^{x} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.310 |
|
|
\[
{}x y^{\prime \prime }-y^{\prime } x -a y = 0
\] |
[_Laguerre] |
✗ |
0.556 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }+y = 0
\] |
[_Laguerre] |
✓ |
1.086 |
|
|
\[
{}x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}x y^{\prime \prime }+\left (b -x \right ) y^{\prime }-a y = 0
\] |
[_Laguerre] |
✗ |
1.007 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.622 |
|
|
\[
{}x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.676 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b +n \right ) y^{\prime }+n a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.135 |
|
|
\[
{}x y^{\prime \prime }-\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.375 |
|
|
\[
{}x y^{\prime \prime }+\left (\left (a +b \right ) x +m +n \right ) y^{\prime }+\left (a b x +a n +b m \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.622 |
|
|
\[
{}x y^{\prime \prime }-2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x +2 a b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.254 |
|
|
\[
{}x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
2.139 |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.418 |
|
|
\[
{}x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.349 |
|
|
\[
{}x y^{\prime \prime }-\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.411 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x^{2}-a \right ) y^{\prime }+2 n x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.154 |
|
|
\[
{}x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.075 |
|
|
\[
{}x y^{\prime \prime }+\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}x y^{\prime \prime }+\left (2 a x \ln \left (x \right )+1\right ) y^{\prime }+\left (a^{2} x \ln \left (x \right )^{2}+a \ln \left (x \right )+a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.316 |
|
|
\[
{}x y^{\prime \prime }+\left (x f \left (x \right )+2\right ) y^{\prime }+f \left (x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.214 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.671 |
|
|
\[
{}2 x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.743 |
|
|
\[
{}2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y = 0
\] |
[_Laguerre] |
✗ |
0.743 |
|
|
\[
{}\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.252 |
|
|
\[
{}4 x y^{\prime \prime }-\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.456 |
|
|
\[
{}4 x y^{\prime \prime }+2 y^{\prime }-y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.265 |
|
|
\[
{}4 x y^{\prime \prime }+4 y^{\prime }-\left (x +2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.082 |
|
|
\[
{}4 x y^{\prime \prime }+4 y-\left (x +2\right ) y+l y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.570 |
|
|
\[
{}4 x y^{\prime \prime }+4 m y^{\prime }-\left (x -2 m -4 n \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.822 |
|
|
\[
{}16 x y^{\prime \prime }+8 y^{\prime }-\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.677 |
|
|
\[
{}a x y^{\prime \prime }+b y^{\prime }+c y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.081 |
|
|
\[
{}a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+3 b y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.345 |
|
|
\[
{}5 \left (a x +b \right ) y^{\prime \prime }+8 a y^{\prime }+c \left (a x +b \right )^{{1}/{5}} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.912 |
|
|
\[
{}2 a x y^{\prime \prime }+\left (b x +a \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.957 |
|
|
\[
{}2 a x y^{\prime \prime }+\left (b x +3 a \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.980 |
|
|
\[
{}\left (\operatorname {a2} x +\operatorname {b2} \right ) y^{\prime \prime }+\left (\operatorname {a1} x +\operatorname {b1} \right ) y^{\prime }+\left (\operatorname {a0} x +\operatorname {b0} \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
7.046 |
|
|
\[
{}x^{2} y^{\prime \prime }-6 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.673 |
|
|
\[
{}x^{2} y^{\prime \prime }-12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.638 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.973 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.830 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.992 |
|
|
\[
{}x^{2} y^{\prime \prime }-\left (a \,x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
3.696 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a^{2} x^{2}-6\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
4.070 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2}-v \left (v -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.098 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{2}+b x +c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.782 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a \,x^{k}-b \left (b -1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.031 |
|
|
\[
{}x^{2} y^{\prime \prime }+\frac {y}{\ln \left (x \right )}-x \,{\mathrm e}^{x} \left (2+x \ln \left (x \right )\right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
0.328 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.478 |
|
|
\[
{}x^{2} y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+a b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.636 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -y-a \,x^{2} = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.772 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +a y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.576 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x +a \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.949 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y = 0
\] |
[_Bessel] |
✓ |
1.034 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (-v^{2}+x^{2}\right ) y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.074 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (l \,x^{2}-v^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.033 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +a \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.476 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +y-3 x^{3} = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.654 |
|
|
\[
{}x^{2} y^{\prime \prime }-y^{\prime } x +\left (a \,x^{m}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.097 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x = 0
\] |
[[_2nd_order, _missing_y]] |
✓ |
0.786 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a x -b^{2}\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.945 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (a \,x^{2}+b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.087 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x +\left (l \,x^{2}+a x -n \left (n +1\right )\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.990 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+a y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.710 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 \left (x +a \right ) y^{\prime }-b \left (b -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.769 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-x^{5} \ln \left (x \right ) = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.105 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y-x \sin \left (x \right )-\left (a \,x^{2}+12 a +4\right ) \cos \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
2.785 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.516 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{2}}{\cos \left (x \right )} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.334 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y-\frac {x^{3}}{\cos \left (x \right )} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
4.453 |
|
|
\[
{}x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (a^{2} x^{2}+2\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
2.690 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (-v^{2}+x^{2}+1\right ) y-f \left (x \right ) = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.074 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (3 x -1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.408 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y-5 x = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.533 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x -5 y-x^{2} \ln \left (x \right ) = 0
\] |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
1.739 |
|
|
\[
{}x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{4}+x^{2} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
1.967 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x -\left (2 x^{3}-4\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.076 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y-\sin \left (x \right ) x^{3} = 0
\] |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
2.384 |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+b y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.923 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+c y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
1.045 |
|
|
\[
{}x^{2} y^{\prime \prime }+a x y^{\prime }+\left (b \,x^{m}+c \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.226 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }+\left (a x +b \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.715 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.970 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x^{2}-1\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.330 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (x -9\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.180 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }+\left (3 x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.431 |
|
|
\[
{}x^{2} y^{\prime \prime }+\left (x +3\right ) x y^{\prime }-y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
0.697 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x -1\right ) y^{\prime }+\left (x -1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.433 |
|