| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y y^{\prime \prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 15 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| \begin{align*}
3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.371 |
|
| \begin{align*}
\sin \left (y\right ) y^{\prime \prime }+\cos \left (y\right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.556 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.671 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=2 y^{\prime } y \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.945 |
|
| \begin{align*}
y^{2} y^{\prime \prime }+y^{\prime \prime }+2 y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.559 |
|
| \begin{align*}
y^{\prime \prime }&=4 x \sqrt {y^{\prime }} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=1 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]] | ✓ | ✓ | ✓ | ✓ | 1.435 |
|
| \begin{align*}
y^{\prime \prime } x&=-y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.546 |
|
| \begin{align*}
-y^{\prime }+y^{\prime \prime } x&=6 x^{5} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.860 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.375 |
|
| \begin{align*}
y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.223 |
|
| \begin{align*}
\left (y-3\right ) y^{\prime \prime }&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.240 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime }&=9 \,{\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.901 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \left (y^{\prime }-2\right ) \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.263 |
|
| \begin{align*}
y^{\prime \prime } x +4 y^{\prime }&=18 x^{2} \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.204 |
|
| \begin{align*}
y^{\prime \prime } x&=2 y^{\prime } \\
y \left (-1\right ) &= 4 \\
y^{\prime }\left (-1\right ) &= 12 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.887 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime } \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.921 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=8 \,{\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.216 |
|
| \begin{align*}
y^{\prime \prime \prime }&=y^{\prime \prime } \\
y \left (0\right ) &= 10 \\
y^{\prime }\left (0\right ) &= 5 \\
y^{\prime \prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.078 |
|
| \begin{align*}
x y^{\prime \prime \prime }+2 y^{\prime \prime }&=6 x \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 1 \\
y^{\prime \prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.194 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=6 \\
y \left (1\right ) &= 4 \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 1.054 |
|
| \begin{align*}
2 x y^{\prime } y^{\prime \prime }&=-1+{y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✓ |
0.554 |
|
| \begin{align*}
3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 9 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.349 |
|
| \begin{align*}
y y^{\prime \prime }+2 {y^{\prime }}^{2}&=3 y^{\prime } y \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= {\frac {3}{4}} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
y^{\prime \prime }&=-{\mathrm e}^{-y} y^{\prime } \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.070 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.345 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.264 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.332 |
|
| \begin{align*}
y^{\prime \prime }&=-2 x {y^{\prime }}^{2} \\
y \left (1\right ) &= -{\frac {1}{4}} \\
y^{\prime }\left (1\right ) &= 5 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
0.492 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.632 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] | ✓ | ✓ | ✗ | ✗ | 0.564 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.591 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime } y \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✗ |
✗ |
0.582 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
4.147 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.309 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }&=4 y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.231 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+4 y&=y^{3} \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.151 |
|
| \begin{align*}
y^{\prime } x +3 y&={\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.715 |
|
| \begin{align*}
y^{\prime \prime \prime }+y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.047 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime \prime }&={y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
0.445 |
|
| \begin{align*}
y^{\prime \prime }&=2 y^{\prime }-5 y+30 \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.422 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.141 |
|
| \begin{align*}
y y^{\prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }&=y \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.106 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-6 y^{\prime } x +12 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.088 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.085 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.086 |
|
| \begin{align*}
y^{\prime \prime }-\left (4+\frac {2}{x}\right ) y^{\prime }+\left (4+\frac {4}{x}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.099 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.097 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{x}-4 x^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.096 |
|
| \begin{align*}
y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.171 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.098 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-2 \cos \left (x \right ) \sin \left (x \right ) y^{\prime }+\left (\cos \left (x \right )^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.106 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.114 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +\left (x^{2}-\frac {1}{4}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.167 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=9 \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.215 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{\prime }+8 y&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-20 y&=27 x^{5} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y^{\prime \prime } x +\left (2 x +2\right ) y^{\prime }+2 y&=8 \,{\mathrm e}^{2 x} \\
\end{align*} | [[_2nd_order, _exact, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✗ | 0.248 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+y^{\prime } x -y&=\left (x +1\right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.217 |
|
| \begin{align*}
y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime \prime }-9 y^{\prime \prime }+27 y^{\prime }-27 y&={\mathrm e}^{3 x} \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.128 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.058 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-4 y^{\prime \prime }+10 y^{\prime }-12 y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.035 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=0 \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.334 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 12 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.114 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }-6 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -9 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 6 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.398 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.231 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 y^{\prime } x -y&=0 \\
y \left (1\right ) &= 8 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.294 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
y \left (1\right ) &= 5 \\
y^{\prime }\left (1\right ) &= 3 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.175 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
y \left (\sqrt {\pi }\right ) &= 3 \\
y^{\prime }\left (\sqrt {\pi }\right ) &= 4 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
5.165 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.309 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.987 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 0.950 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 8 \\
y^{\prime \prime }\left (0\right ) &= 4 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.099 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 4 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \begin{align*}
y^{\prime \prime }-4 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.320 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+9 y&=0 \\
y \left (0\right ) &= 8 \\
y^{\prime }\left (0\right ) &= -24 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.325 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.851 |
|
| \begin{align*}
y^{\prime \prime \prime }-9 y^{\prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.040 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-10 y^{\prime \prime }+9 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.049 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }+10 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-24 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.197 |
|
| \begin{align*}
y^{\prime \prime }-25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.094 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.779 |
|
| \begin{align*}
4 y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.019 |
|
| \begin{align*}
3 y^{\prime \prime }+7 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.339 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.319 |
|
| \begin{align*}
y^{\prime \prime }-8 y^{\prime }+15 y&=0 \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 19 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.322 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.359 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} | [[_2nd_order, _missing_x]] | ✓ | ✓ | ✓ | ✓ | 0.634 |
|
| \begin{align*}
y^{\prime \prime }-9 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.804 |
|
| \begin{align*}
y^{\prime \prime }-10 y^{\prime }+25 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.252 |
|