| # |
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]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.207 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \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]] |
✗ |
✓ |
✗ |
✓ |
4.645 |
|
| \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]] |
✗ |
✓ |
✗ |
✓ |
18.355 |
|
| \begin{align*}
y^{\prime \prime }-y&=1 \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✓ |
23.957 |
|
| \begin{align*}
y^{\prime \prime }-y&=-2 \cos \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✗ |
✓ |
7.044 |
|
| \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]] |
✗ |
✓ |
✓ |
✓ |
2.948 |
|
| \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]] |
✗ |
✓ |
✗ |
✓ |
4.254 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-5 y&=1 \\
y \left (\infty \right ) &= -{\frac {1}{5}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \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]] |
✗ |
✓ |
✗ |
✓ |
5.637 |
|
| \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]] |
✗ |
✓ |
✗ |
✓ |
5.123 |
|
| \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]] |
✗ |
✓ |
✗ |
✗ |
3.974 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
26.832 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.490 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }+6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
44.965 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.112 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.239 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 x y^{\prime }+3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
34.692 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }&=2 y^{\prime } \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.293 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.342 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.586 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-3 x^{2} y^{\prime \prime }+6 x y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.177 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }&=6 y \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
0.315 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.488 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (2 x -3\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.283 |
|
| \begin{align*}
x^{2} \left (\ln \left (x \right )-1\right ) y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.549 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
8.914 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-y+1&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.456 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=5 x^{4} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.589 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.655 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=x \,{\mathrm e}^{2 x}-1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.967 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.504 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
4.179 |
|
| \begin{align*}
x \left (x -1\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]] |
✓ |
✓ |
✓ |
✗ |
1.453 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\frac {1}{\cos \left (2 x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.720 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.825 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {2 \,{\mathrm e}^{x}}{{\mathrm e}^{x}-1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.654 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {1}{1+{\mathrm e}^{x}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.614 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\sqrt {\sin \left (x \right )^{5} \cos \left (x \right )}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.736 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{\cos \left (2 x \right )^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.121 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.013 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.630 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{2}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.844 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }+2 y&=\frac {{\mathrm e}^{-x}}{\sin \left (x \right )} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.648 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.517 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=-\frac {1}{x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.270 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\frac {2 x}{\left (x +1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.798 |
|
| \begin{align*}
y^{\prime \prime }+y&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x^{2}+1\right ) y^{\prime }&=4 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.005 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.217 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime \prime }-y^{\prime }&=\ln \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.666 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }&=-4 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.942 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-x y^{\prime }+y&=\left (x -1\right )^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.611 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y \,{\mathrm e}^{-2 x}&={\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.283 |
|
| \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 (x -1\right )^{2}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.214 |
|
| \begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime \prime }+2 \sin \left (x \right ) y^{\prime }-y \left (\cos \left (x \right )+\sin \left (x \right )\right )&={\mathrm e}^{x} \left (\cos \left (x \right )-\sin \left (x \right )\right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.273 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }-4 x^{3} y&=16 x^{3} {\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.278 |
|
| \begin{align*}
x \left (1-x \ln \left (x \right )\right ) y^{\prime \prime }+\left (1+x^{2} \ln \left (x \right )\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]] |
✗ |
✓ |
✓ |
✗ |
98.677 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
16.739 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
13.133 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=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]] |
✓ |
✓ |
✓ |
✗ |
1.926 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.209 |
|
| \begin{align*}
4 x y^{\prime \prime }+2 y^{\prime }+y&=\frac {6+x}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
46.219 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }&=\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]] |
✓ |
✓ |
✓ |
✓ |
1.237 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=-\left (x -1\right )^{2} {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.682 |
|
| \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]] |
✗ |
✓ |
✗ |
✗ |
14.738 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.164 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
80.342 |
|
| \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 x -2 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
58.539 |
|
| \begin{align*}
x^{\prime \prime }+x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.415 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.391 |
|
| \begin{align*}
x^{\prime \prime }+{x^{\prime }}^{2}+x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.470 |
|
| \begin{align*}
x^{\prime \prime }-2 {x^{\prime }}^{2}+x^{\prime }-2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
30.247 |
|
| \begin{align*}
x^{\prime \prime }-x \,{\mathrm e}^{x^{\prime }}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
3.823 |
|
| \begin{align*}
x^{\prime \prime }+{\mathrm e}^{-x^{\prime }}-x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
37.021 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.571 |
|
| \begin{align*}
x^{\prime \prime }+\left (x+2\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]] |
✓ |
✓ |
✓ |
✗ |
1.272 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }+x-x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
54.038 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.026 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.142 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
y \left (0\right ) &= 0 \\
y \left (2 \pi \right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
3.404 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
33.503 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
4.957 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
6.982 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
8.636 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
33.458 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
2.647 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
3.336 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.210 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.155 |
|