| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=-2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.187 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\
y \left (0\right ) &= -1 \\
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, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=2 x \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=8 \,{\mathrm e}^{x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
y^{\prime \prime \prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+y&=\sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
103.564 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=4 \cos \left (2 x \right )+\sin \left (2 x \right ) \\
y \left (-\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
135.973 |
|
| \begin{align*}
y^{\prime \prime }-y&=1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✓ |
274.464 |
|
| \begin{align*}
y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
100.090 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✓ |
54.073 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+3 y&=8 \,{\mathrm e}^{x}+9 \\
y \left (-\infty \right ) &= 3 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✓ |
41.143 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-5 y&=1 \\
y \left (\infty \right ) &= -{\frac {1}{5}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.215 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }+4 y&=2 \,{\mathrm e}^{x} \left (\sin \left (x \right )+7 \cos \left (x \right )\right ) \\
y \left (-\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
45.098 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{-2 x} \left (9 \sin \left (2 x \right )+8 \cos \left (2 x \right )\right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
93.823 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=\left (9 x^{2}-3 x -4\right ) {\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
60.773 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
18.901 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
16.064 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
21.783 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.706 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }+3 \left (x -2\right ) y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
9.287 |
|
| \begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
12.491 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
23.687 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.224 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.944 |
|
| \begin{align*}
\left (2 x +1\right )^{2} y^{\prime \prime \prime }+2 \left (2 x +1\right ) y^{\prime \prime }+2 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
3.313 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 y^{\prime } x -6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.346 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }&=6 y \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.470 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
7.427 |
|
| \begin{align*}
\left (2 x^{2}+3 x \right ) y^{\prime \prime }-6 \left (x +1\right ) y^{\prime }+6 y&=6 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.263 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.648 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.521 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
29.181 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x -y+1&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
18.626 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x -3 y&=5 x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.218 |
|
| \begin{align*}
\left (4 x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x -1\right ) y^{\prime }-4 y&=12 x^{2}-6 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
11.158 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+{\mathrm e}^{2 x} y&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
19.644 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }&=\frac {\cos \left (x \right )^{2}}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.701 |
|
| \begin{align*}
\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y&=6 \ln \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
66.339 |
|
| \begin{align*}
x \left (-1+x \right ) y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+2 y&=x^{2} \left (2 x -3\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.532 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\frac {1}{\cos \left (2 x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.615 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.717 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {2 \,{\mathrm e}^{x}}{{\mathrm e}^{x}-1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.899 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.786 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
12.194 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
8.276 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }+2 y&=\frac {2 x^{3}+x^{2}-4 x -6}{x^{4}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.476 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\left (\sin \left (x \right )^{7} \cos \left (x \right )^{8}\right )^{{1}/{3}}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
14.358 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.073 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.851 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
6.056 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {2 x}{\left (x +1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.685 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.707 |
|
| \begin{align*}
y^{\prime \prime } x -\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
12.047 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.898 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
4.928 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
4.962 |
|
| \begin{align*}
\left (-1+x \right ) y^{\prime \prime }-y^{\prime } x +y&=\left (-1+x \right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
11.638 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
18.507 |
|
| \begin{align*}
\left (x^{4}-x^{3}\right ) y^{\prime \prime }+\left (2 x^{3}-2 x^{2}-x \right ) y^{\prime }-y&=\frac {\left (-1+x \right )^{2}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.195 |
|
| \begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }+2 \sin \left (x \right ) y^{\prime }-\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&={\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
77.174 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
28.643 |
|
| \begin{align*}
x \left (1-x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+\ln \left (x \right ) x^{2}\right ) y^{\prime }-\left (x +1\right ) y&=\left (1-x \ln \left (x \right )\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
256.622 |
|
| \begin{align*}
4 \left (x^{2}+x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }-y&=2 \sqrt {x^{2}+x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
52.319 |
|
| \begin{align*}
\cos \left (x \right )^{2} y^{\prime \prime }-\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
49.950 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }-\sin \left (x \right ) y&=2 \cos \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= {\frac {1}{2}} \\
y^{\prime }\left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
12.869 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
18.412 |
|
| \begin{align*}
4 y^{\prime \prime } x +2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
222.705 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 y^{\prime } x&=\frac {1}{x^{2}+1} \\
y \left (\infty \right ) &= \frac {\pi ^{2}}{8} \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
10.334 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=-\left (-1+x \right )^{2} {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
26.325 |
|
| \begin{align*}
2 x^{2} \left (2-\ln \left (x \right )\right ) y^{\prime \prime }+x \left (4-\ln \left (x \right )\right ) y^{\prime }-y&=\frac {\left (2-\ln \left (x \right )\right )^{2}}{\sqrt {x}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✗ |
67.511 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}-y&=4 \,{\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y^{\prime }\left (-1\right ) &= -{\mathrm e}^{-1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
16.135 |
|
| \begin{align*}
x^{3} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x^{2} y^{\prime }+y x&=2 \ln \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
154.792 |
|
| \begin{align*}
\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y&=-2+2 x \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.944 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.744 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.420 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.062 |
|
| \begin{align*}
x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
27.636 |
|
| \begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
464.071 |
|
| \begin{align*}
x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.867 |
|
| \begin{align*}
x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
327.924 |
|
| \begin{align*}
x^{\prime \prime }+x {x^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.036 |
|
| \begin{align*}
x^{\prime \prime }+\left (2+x\right ) x^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
6.321 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
328.715 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
42.763 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
20.958 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
169.025 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
y \left (0\right ) &= v_{1} \\
y \left (x_{0} \right ) &= v_{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
99.264 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=0 \\
y \left (0\right ) &= v \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
57.523 |
|
| \begin{align*}
y^{\prime \prime }-\alpha ^{2} s y&=0 \\
y \left (0\right ) &= \frac {1}{s} \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
88.606 |
|
| \begin{align*}
y^{\prime \prime }-\alpha ^{2} s y&=0 \\
y \left (0\right ) &= -\frac {1}{s} \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
61.786 |
|
| \begin{align*}
y^{\prime \prime }&=\alpha ^{2} s^{2} y+\alpha ^{2} g L \\
y \left (0\right ) &= 0 \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
130.947 |
|
| \begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
62.369 |
|
| \begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y \left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
30.456 |
|
| \begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
45.119 |
|
| \begin{align*}
y^{\prime \prime }-\lambda ^{2} y&=0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \frac {1}{\lambda } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
50.104 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.059 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-\lambda ^{4} y&=0 \\
y \left (0\right ) &= 0 \\
y \left (\pi \right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime }\left (\pi \right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.898 |
|
| \begin{align*}
y^{\prime \prime \prime }+\alpha y^{\prime \prime }-\alpha ^{2} y^{\prime }-\alpha ^{3} y&=0 \\
y \left (0\right ) &= -\frac {1}{\alpha } \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1+\frac {1}{\alpha } \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.850 |
|