| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }+3 y^{\prime \prime }+2 y^{\prime }&=\cos \left (t \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.368 |
|
| \begin{align*}
y^{\left (6\right )}+y^{\prime \prime \prime \prime }&=-24 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\tan \left (t \right )^{2} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.221 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }&=3 t^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\sec \left (t \right )^{2} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✗ |
✓ |
✓ |
1.367 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sec \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=\cos \left (t \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.974 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=t \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 1 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.480 |
|
| \begin{align*}
t^{2} \ln \left (t \right ) y^{\prime \prime \prime }-t y^{\prime \prime }+y^{\prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.334 |
|
| \begin{align*}
\left (t^{2}+t \right ) y^{\prime \prime \prime }+\left (-t^{2}+2\right ) y^{\prime \prime }-\left (t +2\right ) y^{\prime }&=-t -2 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.365 |
|
| \begin{align*}
2 t^{3} y^{\prime \prime \prime }+t^{2} y^{\prime \prime }+y^{\prime } t -y&=-3 t^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.676 |
|
| \begin{align*}
t y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }&=\frac {45}{8 t^{{7}/{2}}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 1 \\
y^{\prime \prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.359 |
|
| \begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.766 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.958 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-8 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.171 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.229 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+17 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }-9 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.117 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-2 y^{\prime } x +20 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.841 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.740 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.624 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.629 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+7 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.398 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+22 x^{2} y^{\prime \prime }+124 y^{\prime } x +140 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-4 x^{2} y^{\prime \prime }-46 y^{\prime } x +100 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-4 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }+6 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.460 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+6 x^{2} y^{\prime \prime }+7 y^{\prime } x +y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime \prime }+6 x^{2} y^{\prime \prime \prime }+7 y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.680 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=\frac {1}{x^{5}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.299 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.302 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
21.378 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
14.141 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y&=2 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.921 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -16 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.190 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.494 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +36 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.026 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-11 y^{\prime } x +16 y&=\frac {1}{x^{3}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+70 y^{\prime } x +80 y&=\frac {1}{x^{13}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.661 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-4 y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.163 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-7 y^{\prime } x +7 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
6.619 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
y \left (1\right ) &= -1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.178 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.432 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+10 x^{2} y^{\prime \prime }-20 y^{\prime } x +20 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
y^{\prime \prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.381 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+54 y^{\prime } x +42 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.338 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }+5 y^{\prime } x -5 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.351 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-6 x^{2} y^{\prime \prime }+17 y^{\prime } x -17 y&=0 \\
y \left (1\right ) &= -2 \\
y^{\prime }\left (1\right ) &= 0 \\
y^{\prime \prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.335 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+3 y^{\prime } x -y&=\frac {1}{x^{2}} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=\ln \left (x \right ) \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
48.311 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=x^{3} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.809 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y&=\frac {1}{x} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
67.014 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.787 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.520 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.833 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }+37 y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.478 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.414 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.394 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+3 x^{2} y^{\prime \prime }-3 y^{\prime } x&=-8 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.568 |
|
| \begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.226 |
|
| \begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.717 |
|
| \begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.773 |
|
| \begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=\arctan \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.283 |
|
| \begin{align*}
\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.128 |
|
| \begin{align*}
\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (4 x^{2}-4\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.229 |
|
| \begin{align*}
\left (x^{4}-1\right ) y^{\prime \prime }+\left (x^{3}-x \right ) y^{\prime }+\left (x^{2}-1\right ) y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.921 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +4 y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
20.466 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (-1\right ) &= 0 \\
y^{\prime }\left (-1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.849 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+16 x^{2} y^{\prime \prime }+79 y^{\prime } x +125 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.330 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+5 x^{3} y^{\prime \prime \prime }-12 x^{2} y^{\prime \prime }-12 y^{\prime } x +48 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.496 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+14 x^{3} y^{\prime \prime \prime }+55 x^{2} y^{\prime \prime }+65 y^{\prime } x +15 y&=0 \\
\end{align*} |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.497 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+8 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+35 y^{\prime } x +45 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.481 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+10 x^{3} y^{\prime \prime \prime }+27 x^{2} y^{\prime \prime }+21 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }+44 y^{\prime } x +58 y&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 10 \\
y^{\prime \prime }\left (1\right ) &= -2 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+5 y^{\prime } x -y&=0 \\
y \left (1\right ) &= a \\
y^{\prime }\left (1\right ) &= b \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.773 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +7 y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.243 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=-2\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.270 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime \prime }+16 \left (2+x \right ) y^{\prime }-y&=0 \\
\end{align*}
Series expansion around \(x=1\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.339 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-18 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.107 |
|
| \begin{align*}
y^{\prime \prime }-11 y^{\prime }+30 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.121 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-x} \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.126 |
|
| \begin{align*}
\left (-2-2 x \right ) y^{\prime \prime }+2 y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \begin{align*}
\left (3 x +2\right ) y^{\prime \prime }+3 y^{\prime } x&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.875 |
|
| \begin{align*}
\left (1+3 x \right ) y^{\prime \prime }-3 y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.049 |
|
| \begin{align*}
\left (-x^{2}+2\right ) y^{\prime \prime }+2 \left (x -1\right ) y^{\prime }+4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.178 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +4 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.769 |
|
| \begin{align*}
\left (2 x^{2}+2\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.929 |
|
| \begin{align*}
\left (3-2 x \right ) y^{\prime \prime }+2 y^{\prime }-2 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.877 |
|
| \begin{align*}
y^{\prime \prime }-4 x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.611 |
|
| \begin{align*}
\left (2 x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -3 y&=0 \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.799 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.712 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y x&=\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }+\left (-1+y^{2}\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x], _Van_der_Pol] |
✓ |
✓ |
✗ |
✗ |
0.477 |
|
| \begin{align*}
y^{\prime \prime }+\left (\frac {{y^{\prime }}^{2}}{3}-1\right ) y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
0.470 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.704 |
|