| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.247 |
|
| \begin{align*}
4 y^{\prime \prime }-4 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|
| \begin{align*}
25 y^{\prime \prime }-10 y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
16 y^{\prime \prime }-24 y^{\prime }+9 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.254 |
|
| \begin{align*}
9 y^{\prime \prime }+12 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.251 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.401 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+16 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 14 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.408 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.389 |
|
| \begin{align*}
4 y^{\prime \prime }+4 y^{\prime }+y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
y^{\prime \prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.775 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.250 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+5 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+29 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.266 |
|
| \begin{align*}
9 y^{\prime \prime }+18 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.259 |
|
| \begin{align*}
4 y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.765 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 14.247 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
y^{\prime \prime }+16 y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.112 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.436 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+13 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 31 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.380 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.437 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+\left (\frac {1}{4}+4 \pi ^{2}\right ) y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.439 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.048 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-34 y^{\prime \prime }+225 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-81 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-18 y^{\prime \prime }+81 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\left (5\right )}+18 y^{\prime \prime \prime }+81 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.067 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.054 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y^{\prime \prime }+37 y^{\prime }-50 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
y^{\prime \prime \prime }-9 y^{\prime \prime }+31 y^{\prime }-39 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+2 y^{\prime \prime }+4 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.060 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }+10 y^{\prime \prime }+18 y^{\prime }+9 y&=0 \\
\end{align*} | [[_high_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.060 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 6 \\
y^{\prime \prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 13 \\
y^{\prime \prime }\left (0\right ) &= 86 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.084 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+26 y^{\prime \prime }+25 y&=0 \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= -28 \\
y^{\prime \prime }\left (0\right ) &= -102 \\
y^{\prime \prime \prime }\left (0\right ) &= 622 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }+9 y^{\prime \prime }+9 y^{\prime }&=0 \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
y^{\prime \prime \prime }\left (0\right ) &= -60 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
y^{\prime \prime \prime }+216 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-3 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+13 y^{\prime \prime }+36 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.066 |
|
| \begin{align*}
y^{\left (6\right )}-2 y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
16 y^{\prime \prime \prime \prime }-y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
4 y^{\prime \prime \prime \prime }+15 y^{\prime \prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.052 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+16 y^{\prime }-16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.056 |
|
| \begin{align*}
y^{\left (6\right )}+16 y^{\prime \prime \prime }+64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.082 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +8 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.920 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.358 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.079 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +9 y&=0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.771 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.777 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-19 y^{\prime } x +100 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.778 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 y^{\prime } x +29 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.026 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +29 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.842 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.158 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+37 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 y^{\prime } x +5 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.014 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }-7 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.873 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -10 y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (4\right ) &= 0 \\
y^{\prime }\left (4\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-11 y^{\prime } x +36 y&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (1\right ) &= 2 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.064 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.266 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 1.336 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +13 y&=0 \\
y \left (1\right ) &= 9 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.269 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.102 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-5 x^{2} y^{\prime \prime }+14 y^{\prime } x -18 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.103 |
|
| \begin{align*}
-8 y+7 y^{\prime } x -3 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+15 x^{2} y^{\prime \prime }+9 y^{\prime } x +16 y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }-9 y^{\prime } x +9 y&=0 \\
\end{align*} |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+2 x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+7 x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_high_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=24 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.468 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.440 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-8 y&=8 x^{2}-3 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.418 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=36 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.188 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-6 \,{\mathrm e}^{4 x} \\
y \left (0\right ) &= 6 \\
y^{\prime }\left (0\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=7 \,{\mathrm e}^{5 x} \\
y \left (0\right ) &= 12 \\
y^{\prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.510 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+9 y&=169 \sin \left (2 x \right ) \\
y \left (0\right ) &= -10 \\
y^{\prime }\left (0\right ) &= 9 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.678 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=10 x +12 \\
y \left (1\right ) &= 6 \\
y^{\prime }\left (1\right ) &= 8 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.608 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime }&=1 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 3 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 2 \\
\end{align*} | [[_high_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.144 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&={\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.390 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=-18 \,{\mathrm e}^{4 x}+14 \,{\mathrm e}^{5 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-10 y&=35 \,{\mathrm e}^{5 x}+12 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=22 x +24 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.369 |
|