| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }-y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.091 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime \prime }+9 y^{\prime \prime }&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\infty \right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.242 |
|
| \begin{align*}
y^{\prime \prime \prime }+6 y^{\prime \prime }+12 y^{\prime }+y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
y^{\prime \prime }\left (0\right ) &= -2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.238 |
|
| \begin{align*}
8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.095 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-4 y^{\prime \prime }-4 y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+5 y^{\prime \prime }-8 y^{\prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+5 y^{\prime \prime }+4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.106 |
|
| \begin{align*}
-4 y+3 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\left (5\right )}+y^{\prime \prime \prime \prime }-9 y^{\prime \prime \prime }-13 y^{\prime \prime }+8 y^{\prime }+12 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.121 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-11 y^{\prime \prime \prime }+36 y^{\prime \prime }-16 y^{\prime }-64 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
9.683 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+4 y^{\prime \prime \prime }+2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
4 y^{\prime \prime \prime \prime }-24 y^{\prime \prime \prime }+35 y^{\prime \prime }+6 y^{\prime }-9 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
4 y^{\prime \prime \prime \prime }+20 y^{\prime \prime \prime }+35 y^{\prime \prime }+25 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+11 y^{\prime \prime }+5 y^{\prime }-14 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
y^{\prime \prime \prime }+5 y^{\prime \prime }+7 y^{\prime }+3 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.093 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }-2 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
y^{\prime \prime }+y&=1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.162 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=8 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.193 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }+2 y&=5 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.157 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }-5 y&=20 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
22.740 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=3 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.205 |
|
| \begin{align*}
y^{\prime \prime \prime }-5 y^{\prime \prime }+4 y&=14 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime \prime }&=12 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.198 |
|
| \begin{align*}
y^{\prime \prime \prime }-7 y^{\prime \prime }+14 y^{\prime }-8 y&=2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
y^{\prime \prime \prime }+9 y^{\prime }&=11 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.204 |
|
| \begin{align*}
y^{\prime \prime \prime }+9 y^{\prime \prime }&=11 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.191 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+9 y^{\prime \prime \prime }&=11 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }&=12 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.217 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime }&=12 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.240 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }&=12 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.224 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }&=12 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.722 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+9 y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
15.080 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=27 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.605 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }-3 y&=-6 x^{2}-8 x +4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.167 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
32.870 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=15 \,{\mathrm e}^{x}-8 x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
23.354 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.625 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-2 y&=12 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.237 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=2+{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
24.442 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&=6 x +6 \,{\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.023 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=20 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
34.644 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=2 \cos \left (x \right )+4 \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
35.040 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=7+75 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
35.602 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=50 x +13 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.312 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.934 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
33.251 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \left (2 \sin \left (x \right )+4 \cos \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
25.354 |
|
| \begin{align*}
y^{\prime \prime }-y&=8 x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
23.522 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.205 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.582 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-4 y^{\prime }-4 y&=3 \,{\mathrm e}^{-x}-4 x -6 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=7 x^{2} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&={\mathrm e}^{-x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.183 |
|
| \begin{align*}
y^{\prime \prime }-y&=10 \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.779 |
|
| \begin{align*}
y^{\prime \prime }+y&=12 \cos \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=4 \sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.079 |
|
| \begin{align*}
y^{\prime \prime }+y&=10 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.544 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=2-8 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
39.763 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=-18 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.171 |
|
| \begin{align*}
5 y+4 y^{\prime }+y^{\prime \prime }&=10 \,{\mathrm e}^{-3 x} \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
62.811 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=10 \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
64.508 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+5 x&=8 \sin \left (t \right ) \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
26.840 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \\
y \left (0\right ) &= -3 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
19.787 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=x \\
y \left (0\right ) &= -2 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
36.319 |
|
| \begin{align*}
4 y^{\prime \prime }+y&=2 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.819 |
|
| \begin{align*}
2 y^{\prime \prime }-5 y^{\prime }-3 y&=-9 x^{2}-1 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.710 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=x +1 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.750 |
|
| \begin{align*}
y^{\prime \prime }+y&=x^{3} \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
8.465 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.230 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }&=4 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-2 x +2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
5.460 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=\sin \left (3 x \right ) \\
y \left (0\right ) &= 1 \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
65.112 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\sin \left (b x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
25.824 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\sin \left (a x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
25.944 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=4 \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.015 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=15 \cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.192 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=18 x -3+20 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
23.181 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&=42 \,{\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
6.724 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.661 |
|
| \begin{align*}
y^{\prime \prime }+6 y^{\prime }+14 y&=42 \,{\mathrm e}^{x}-7 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
37.473 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.590 |
|
| \begin{align*}
y^{\prime \prime }+y&=4 x +1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.917 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.869 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{x}-x +\sin \left (3 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.214 |
|
| \begin{align*}
y^{\prime \prime }-y&=2 x -3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
11.261 |
|
| \begin{align*}
y^{\prime \prime }-y&=x +\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
12.811 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
23.593 |
|
| \begin{align*}
y^{\prime \prime }-y&=16 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
23.199 |
|
| \begin{align*}
y^{\prime \prime }-y&=\cos \left (4 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.391 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=6 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.941 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
35.906 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=4-{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
36.551 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
23.074 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
20.569 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
15.510 |
|