|
# |
ODE |
CAS classification |
Solved? |
time (sec) |
|
\[
{}2 x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.908 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.776 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.843 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.827 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
0.807 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+y^{\prime } x -y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.183 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.155 |
|
|
\[
{}9 x^{2} y^{\prime \prime }+2 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
0.736 |
|
|
\[
{}2 x^{2} y^{\prime \prime }+5 y^{\prime } x -2 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.095 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 y^{\prime } x -12 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.059 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -9 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.013 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.171 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.132 |
|
|
\[
{}x^{2} y^{\prime \prime }+5 y^{\prime } x +5 y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
2.015 |
|
|
\[
{}x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y = 0
\] |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
0.139 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.941 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+\left (1-2 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.993 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.914 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (4 x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.825 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.872 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (1+3 x \right ) y^{\prime }+\left (1-6 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.983 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x -1\right ) y^{\prime }+\left (1-x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.916 |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.897 |
|
|
\[
{}x \left (x -2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.955 |
|
|
\[
{}4 \left (x -4\right )^{2} y^{\prime \prime }+\left (x -4\right ) \left (x -8\right ) y^{\prime }+x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.128 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.916 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.723 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }-x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.779 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2 x +3\right ) y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.025 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+8 x \left (x +1\right ) y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.047 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 x \left (x +1\right ) y^{\prime }+\left (1-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.068 |
|
|
\[
{}x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.921 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x \left (x -2\right ) y^{\prime }+2 \left (2-3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.108 |
|
|
\[
{}x^{2} \left (2 x +1\right ) y^{\prime \prime }+2 x \left (1+6 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.250 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (2+3 x \right ) y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.098 |
|
|
\[
{}x y^{\prime \prime }-\left (x +3\right ) y^{\prime }+2 y = 0
\] |
[_Laguerre] |
✓ |
1.052 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.140 |
|
|
\[
{}x \left (x +1\right ) y^{\prime \prime }+\left (5+x \right ) y^{\prime }-4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.257 |
|
|
\[
{}x^{2} y^{\prime \prime }+x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.089 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.995 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }-3 y^{\prime }+2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.129 |
|
|
\[
{}x y^{\prime \prime }+\left (4+3 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.026 |
|
|
\[
{}x y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.100 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.036 |
|
|
\[
{}x \left (x +3\right ) y^{\prime \prime }-9 y^{\prime }-6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.009 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.118 |
|
|
\[
{}x y^{\prime \prime }+\left (x^{3}-1\right ) y^{\prime }+x^{2} y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.896 |
|
|
\[
{}x^{2} \left (4 x -1\right ) y^{\prime \prime }+x \left (1+5 x \right ) y^{\prime }+3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.226 |
|
|
\[
{}x y^{\prime \prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.265 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +\left (3+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.441 |
|
|
\[
{}2 x y^{\prime \prime }+6 y^{\prime }+y = 0
\] |
[[_Emden, _Fowler]] |
✓ |
1.344 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x \left (2-x \right ) y^{\prime }-\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.524 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (6+x \right ) y^{\prime }+10 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.520 |
|
|
\[
{}x y^{\prime \prime }+\left (2 x +3\right ) y^{\prime }+8 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.420 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.387 |
|
|
\[
{}x \left (1-x \right ) y^{\prime \prime }+2 \left (1-x \right ) y^{\prime }+2 y = 0
\] |
[_Jacobi] |
✓ |
1.397 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
0.897 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-1\right ) y = 0
\] |
[_Bessel] |
✓ |
1.278 |
|
|
\[
{}x^{2} y^{\prime \prime }-5 y^{\prime } x +\left (8+5 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.482 |
|
|
\[
{}x y^{\prime \prime }+\left (3-x \right ) y^{\prime }-5 y = 0
\] |
[_Laguerre] |
✓ |
1.390 |
|
|
\[
{}9 x^{2} y^{\prime \prime }-15 y^{\prime } x +7 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.543 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (1-2 x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.540 |
|
|
\[
{}x^{2} y^{\prime \prime }+3 y^{\prime } x +\left (x^{3}+x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.060 |
|
|
\[
{}2 x \left (1-x \right ) y^{\prime \prime }+\left (1-2 x \right ) y^{\prime }+\left (x +2\right ) y = 0
\] |
[_Jacobi] |
✓ |
1.274 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime }+x \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.840 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +1\right ) y^{\prime }-\left (6 x^{2}-3 x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.271 |
|
|
\[
{}x y^{\prime \prime }+y^{\prime } x +\left (x^{4}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.291 |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.074 |
|
|
\[
{}x \left (x -2\right )^{2} y^{\prime \prime }-2 \left (x -2\right ) y^{\prime }+2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.895 |
|
|
\[
{}2 x y^{\prime \prime }+\left (1-x \right ) y^{\prime }-\left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.092 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.336 |
|
|
\[
{}x y^{\prime \prime }-\left (x +2\right ) y^{\prime }-2 y = 0
\] |
[_Laguerre] |
✓ |
1.398 |
|
|
\[
{}x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-2 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.105 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +7\right ) y^{\prime }+2 \left (5+x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.121 |
|
|
\[
{}x^{2} \left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (x^{2}+3\right ) y^{\prime }+6 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.035 |
|
|
\[
{}\left (-x^{2}+1\right ) y^{\prime \prime }-10 y^{\prime } x -18 y = 0
\] |
[_Gegenbauer] |
✓ |
0.691 |
|
|
\[
{}2 x y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-3 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.096 |
|
|
\[
{}y^{\prime \prime }+2 y^{\prime } x -8 y = 0
\] |
[_erf] |
✓ |
0.633 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }-\left (x^{2}+7\right ) y^{\prime }+4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
1.029 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+4 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.174 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-2 x \left (x +2\right ) y^{\prime }+\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.127 |
|
|
\[
{}x^{2} y^{\prime \prime }-x \left (x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.907 |
|
|
\[
{}2 x y^{\prime \prime }+y^{\prime }+y = 0
\] |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
1.098 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x^{2}-3\right ) y^{\prime }+4 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.811 |
|
|
\[
{}4 x^{2} y^{\prime \prime }-x^{2} y^{\prime }+y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.040 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime \prime }-2 y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.639 |
|
|
\[
{}2 x^{2} y^{\prime \prime }-x \left (2 x +1\right ) y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.255 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+3 x^{2} y^{\prime }+\left (1+3 x \right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.077 |
|
|
\[
{}x y^{\prime \prime }+\left (-x^{2}+1\right ) y^{\prime }+2 x y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.773 |
|
|
\[
{}4 x^{2} y^{\prime \prime }+2 x^{2} y^{\prime }-\left (x +3\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.107 |
|
|
\[
{}x \left (-x^{2}+1\right ) y^{\prime \prime }+5 \left (-x^{2}+1\right ) y^{\prime }-4 x y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.961 |
|
|
\[
{}x^{2} y^{\prime \prime }+x \left (x +3\right ) y^{\prime }+\left (2 x +1\right ) y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.991 |
|
|
\[
{}x^{2} y^{\prime \prime }+y^{\prime } x -\left (x^{2}+4\right ) y = 0
\] |
[[_Bessel, _modified]] |
✓ |
1.267 |
|
|
\[
{}x \left (1-2 x \right ) y^{\prime \prime }-2 \left (x +2\right ) y^{\prime }+18 y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
1.116 |
|
|
\[
{}x y^{\prime \prime }+\left (2-x \right ) y^{\prime }-y = 0
\] |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
0.972 |
|
|
\[
{}x^{2} y^{\prime \prime }-3 y^{\prime } x +4 \left (x +1\right ) y = 0
\] |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
0.915 |
|
|
\[
{}y^{\prime } = \frac {y}{x \ln \left (x \right )}
\] |
[_separable] |
✓ |
1.595 |
|
|
\[
{}\left (x^{2}+1\right ) y^{\prime }+y^{2} = -1
\] |
[_separable] |
✓ |
2.767 |
|
|
\[
{}y^{\prime }+\frac {2 y}{x} = 5 x^{2}
\] |
[_linear] |
✓ |
1.678 |
|
|
\[
{}t x^{\prime }+2 x = 4 \,{\mathrm e}^{t}
\] |
[_linear] |
✓ |
1.299 |
|