| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+6 x +2\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.856 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} y&=\sec \left (a x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.340 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.855 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.126 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\cot \left (x \right )\right ) y^{\prime }-\cot \left (x \right ) y&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
2.859 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
x^{\prime }-7 x+y&=0 \\
y^{\prime }-2 x-5 y&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.545 |
|
| \begin{align*}
x^{\prime }+5 x+y&={\mathrm e}^{t} \\
y^{\prime }-x+3 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
4 x^{\prime }+9 y^{\prime }+11 x+31 y&={\mathrm e}^{t} \\
3 x^{\prime }+7 y^{\prime }+8 x+24 y&={\mathrm e}^{2 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.659 |
|
| \begin{align*}
t x^{\prime }&=t -2 x \\
t y^{\prime }&=t x+t y+2 x-t \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.035 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.276 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {1-y^{2}}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
134.348 |
|
| \begin{align*}
y^{\prime } x&=y \left (1-2 y\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.683 |
|
| \begin{align*}
y^{\prime }-y \sin \left (x \right )&=\sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.550 |
|
| \begin{align*}
y^{\prime } x -2 y&=x^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.862 |
|
| \begin{align*}
s^{\prime }+2 s&=s t^{2} \\
s \left (0\right ) &= 1 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.554 |
|
| \begin{align*}
x^{\prime }-2 x&={\mathrm e}^{2 t} t \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.062 |
|
| \begin{align*}
y^{\prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.489 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{3} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.311 |
|
| \begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2}+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
26.973 |
|
| \begin{align*}
x +y^{2}-2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.126 |
|
| \begin{align*}
\sin \left (y x \right )+x y \cos \left (y x \right )+x^{2} \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact] |
✓ |
✓ |
✓ |
✓ |
24.533 |
|
| \begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.992 |
|
| \begin{align*}
2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
11.938 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}-\frac {x}{1+y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.279 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y^{\prime }} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.809 |
|
| \begin{align*}
y&=2 y^{\prime } x +\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.890 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.310 |
|
| \begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.215 |
|
| \begin{align*}
y^{\prime } x -y^{2}+\left (2 x +1\right ) y&=x^{2}+2 x \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
9.926 |
|
| \begin{align*}
{\mathrm e}^{-x} y^{\prime }+y^{2}-2 \,{\mathrm e}^{x} y&=1-{\mathrm e}^{2 x} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
279.825 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.954 |
|
| \begin{align*}
x^{2}-y x +y^{2}-x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
49.556 |
|
| \begin{align*}
y x -\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 7.856 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.056 |
|
| \begin{align*}
20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.218 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }+4 y&=0 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.706 |
|
| \begin{align*}
8 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]] |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
x^{\prime \prime }-x^{\prime }-6 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.243 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x -4 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.088 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.522 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✗ |
0.973 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.248 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.702 |
|
| \begin{align*}
x^{\prime \prime }-3 x^{\prime }+2 x&=6 \,{\mathrm e}^{3 t} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.370 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=10 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=5+10 \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.361 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-6 y&=3 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.462 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right )^{3} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.003 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.008 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x}+1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.649 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+4 y&=6 x \,{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.872 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=\cos \left ({\mathrm e}^{x}\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.540 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.004 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=0 \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.339 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.962 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.897 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.637 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.213 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -3 y&=3 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.301 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }+5 y^{\prime } x +y&=x^{2}+x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.957 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +4 y&=2 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +3 y&=5 x^{2} \\
y \left (1\right ) &= 3 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
27.446 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=20 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.668 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \sin \left (3 x \right ) \\
y \left (0\right ) &= 5 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.772 |
|
| \begin{align*}
y^{\prime \prime }+y&=1+2 \cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} | [[_2nd_order, _linear, _nonhomogeneous]] | ✓ | ✓ | ✓ | ✓ | 0.838 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=3 x^{2}-x \\
y \left (1\right ) &= \pi \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.999 |
|
| \begin{align*}
x^{\prime \prime }+x&=5 t^{2} \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
x^{\prime \prime }+x&=2 \tan \left (t \right ) \\
x \left (0\right ) &= 4 \\
x^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.270 |
|
| \begin{align*}
y^{\prime \prime }-k^{2} y&=f \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.314 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{-x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.603 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x -15 y&={\mathrm e}^{x} x^{4} \\
y \left (1\right ) &= 1 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.712 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
y^{\prime }&=2 y x -x^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y p \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y^{2}+x^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} Series expansion around \(x=0\). |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.269 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.323 |
|
| \begin{align*}
y^{\prime }&=y-x \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.263 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y p \\
\end{align*} Series expansion around \(x=0\). |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.304 |
|
| \begin{align*}
y^{\prime \prime }+9 y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.307 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y^{\prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.356 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x +3 y&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[_Hermite] |
✓ |
✓ |
✓ |
✓ |
0.575 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime } x +y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.585 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} Series expansion around \(x=1\). | [[_Emden, _Fowler]] | ✓ | ✓ | ✓ | ✓ | 0.553 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.400 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.615 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.669 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x \left (1-x \right ) y^{\prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.601 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+\frac {3 y^{\prime }}{2+x}+\frac {\left (1-x \right )^{2} y}{x +3}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.790 |
|
| \begin{align*}
\frac {y^{\prime \prime }}{x}+\frac {3 \left (x -4\right ) y^{\prime }}{6+x}+\frac {x^{2} \left (x -2\right ) y}{x -1}&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
x^{2} \left (x -2\right ) y^{\prime \prime }+4 \left (x -2\right ) y^{\prime }+3 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.254 |
|