| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime }+\left (a \cosh \left (x \right )^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.586 |
|
| \begin{align*}
y^{\prime \prime }+\left (a \cos \left (2 x \right )+b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✗ |
✓ |
✓ |
✗ |
3.211 |
|
| \begin{align*}
y^{\prime \prime }+\left (\cos \left (x \right )^{2} a +b \right ) y&=0 \\
\end{align*} |
[_ellipsoidal] |
✗ |
✓ |
✓ |
✗ |
3.333 |
|
| \begin{align*}
y^{\prime \prime }-\left (1+2 \tan \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.692 |
|
| \begin{align*}
y^{\prime \prime }-\left (\frac {m \left (m -1\right )}{\cos \left (x \right )^{2}}+\frac {n \left (n -1\right )}{\sin \left (x \right )^{2}}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
8.611 |
|
| \begin{align*}
y^{\prime \prime }-\left (n \left (n +1\right ) k^{2} \operatorname {JacobiSN}\left (x , k\right )^{2}+b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.668 |
|
| \begin{align*}
y^{\prime \prime }-\left (f \left (x \right )^{2}+f^{\prime }\left (x \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.435 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+a \,{\mathrm e}^{-2 x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.394 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }+y \,{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.075 |
|
| \begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.870 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+b y-f \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }-\left (b^{2} x^{2}+c \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.337 |
|
| \begin{align*}
y^{\prime \prime }+2 a y^{\prime }+f \left (x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
4.966 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.257 |
|
| \begin{align*}
-y+x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.368 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }+\left (n +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.309 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }-n y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.873 |
|
| \begin{align*}
2 y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✓ |
✓ |
✓ |
✗ |
0.879 |
|
| \begin{align*}
-a y-x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✗ |
✓ |
✓ |
✗ |
4.946 |
|
| \begin{align*}
y^{\prime \prime }-x y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.640 |
|
| \begin{align*}
y^{\prime \prime }-2 x y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.996 |
|
| \begin{align*}
y^{\prime \prime }+4 x y^{\prime }+\left (4 x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.658 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (3 x^{2}+2 n -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.663 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-1\right ) y-{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.688 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.634 |
|
| \begin{align*}
y^{\prime \prime }-4 x y^{\prime }+\left (4 x^{2}-3\right ) y-{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| \begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.480 |
|
| \begin{align*}
y^{\prime \prime }+2 a x y^{\prime }+a^{2} x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.132 |
|
| \begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.147 |
|
| \begin{align*}
y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (\operatorname {a1} \,x^{2}+\operatorname {b1} x +\operatorname {c1} \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.157 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.460 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-\left (x +1\right )^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.557 |
|
| \begin{align*}
-x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.019 |
|
| \begin{align*}
y^{\prime \prime }+a \,x^{-1+q} y^{\prime }+b \,x^{q -2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.358 |
|
| \begin{align*}
y^{\prime \prime }+\sqrt {x}\, y^{\prime }+\left (\frac {1}{4 \sqrt {x}}+\frac {x}{4}-9\right ) y-x \,{\mathrm e}^{-\frac {x^{{3}/{2}}}{3}}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.496 |
|
| \begin{align*}
y^{\prime \prime }-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y \,{\mathrm e}^{2 x}-{\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.423 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+\tan \left (x \right )+b y&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.501 |
|
| \begin{align*}
y^{\prime \prime }+2 n y^{\prime } \cot \left (x \right )+\left (-a^{2}+n^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.135 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.462 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.959 |
|
| \begin{align*}
y^{\prime \prime }+\cot \left (x \right ) y^{\prime }+v \left (v +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.078 |
|
| \begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }+y \sin \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| \begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.522 |
|
| \begin{align*}
\left (-a^{2}+b^{2}\right ) y+2 a \cot \left (a x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.272 |
|
| \begin{align*}
y^{\prime \prime }+f \left (x \right ) y^{\prime }+\left (\frac {f \left (x \right )^{2}}{4}+\frac {f^{\prime }\left (x \right )}{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.219 |
|
| \begin{align*}
y^{\prime \prime }-\frac {a f^{\prime }\left (x \right ) y^{\prime }}{f \left (x \right )}+b f \left (x \right )^{2 a} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✗ |
✗ |
2.011 |
|
| \begin{align*}
y^{\prime \prime }-\left (\frac {f^{\prime }\left (x \right )}{f \left (x \right )}+2 a \right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) a}{f \left (x \right )}+a^{2}-b^{2} f \left (x \right )^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
8.804 |
|
| \begin{align*}
y^{\prime \prime }-\left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right ) y^{\prime }+\left (\frac {f^{\prime }\left (x \right ) \left (\frac {2 f^{\prime }\left (x \right )}{f \left (x \right )}+\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}-\frac {g^{\prime }\left (x \right )}{g \left (x \right )}\right )}{f \left (x \right )}-\frac {f^{\prime \prime }\left (x \right )}{f \left (x \right )}-\frac {v^{2} {g^{\prime }\left (x \right )}^{2}}{g \left (x \right )^{2}}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.646 |
|
| \begin{align*}
y^{\prime \prime }-\left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right ) y^{\prime }+\left (\frac {h^{\prime }\left (x \right ) \left (\frac {g^{\prime \prime }\left (x \right )}{g^{\prime }\left (x \right )}+\frac {\left (2 v -1\right ) g^{\prime }\left (x \right )}{g \left (x \right )}+\frac {2 h^{\prime }\left (x \right )}{h \left (x \right )}\right )}{h \left (x \right )}-\frac {h^{\prime \prime }\left (x \right )}{h \left (x \right )}+{g^{\prime }\left (x \right )}^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.476 |
|
| \begin{align*}
4 y^{\prime \prime }+9 y x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.344 |
|
| \begin{align*}
4 y^{\prime \prime }-\left (x^{2}+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.879 |
|
| \begin{align*}
4 y^{\prime \prime }+4 \tan \left (x \right ) y^{\prime }-\left (5 \tan \left (x \right )^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.800 |
|
| \begin{align*}
a y^{\prime \prime }-\left (a b +c +x \right ) y^{\prime }+\left (b \left (x +c \right )+d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.679 |
|
| \begin{align*}
a^{2} y^{\prime \prime }+a \left (a^{2}-2 b \,{\mathrm e}^{-a x}\right ) y^{\prime }+b^{2} {\mathrm e}^{-2 a x} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.220 |
|
| \begin{align*}
x \left (y^{\prime \prime }+y\right )-\cos \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.739 |
|
| \begin{align*}
\left (x +a \right ) y+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.728 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.133 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+a y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.411 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+l x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.938 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.518 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+a y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.424 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }-a \,x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.442 |
|
| \begin{align*}
x y^{\prime \prime }-y^{\prime }+x^{3} \left ({\mathrm e}^{x^{2}}-v^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.163 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x -{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.283 |
|
| \begin{align*}
a x y+2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.948 |
|
| \begin{align*}
a \,x^{2} y+2 y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
x y^{\prime \prime }-2 y^{\prime }+a y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
x y^{\prime \prime }+v y^{\prime }+a y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.531 |
|
| \begin{align*}
b x y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| \begin{align*}
x y^{\prime \prime }+a y^{\prime }+b \,x^{\operatorname {a1}} y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
0.550 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.884 |
|
| \begin{align*}
x y^{\prime \prime }+\left (x +a +b \right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.828 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }-y-x \left (x +1\right ) {\mathrm e}^{x}&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.476 |
|
| \begin{align*}
x y^{\prime \prime }-x y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
4.439 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
0.944 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x +1\right ) y^{\prime }-2 \left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.769 |
|
| \begin{align*}
x y^{\prime \prime }+\left (-x +b \right ) y^{\prime }-a y&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
6.222 |
|
| \begin{align*}
x y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.926 |
|
| \begin{align*}
x y^{\prime \prime }-\left (3 x -2\right ) y^{\prime }-\left (2 x -3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.592 |
|
| \begin{align*}
x y^{\prime \prime }+\left (a x +b +n \right ) y^{\prime }+n a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.844 |
|
| \begin{align*}
x y^{\prime \prime }-\left (a +b \right ) \left (x +1\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
9.059 |
|
| \begin{align*}
\left (a b x +a n +b m \right ) y+\left (m +n +x \left (a +b \right )\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
10.425 |
|
| \begin{align*}
x y^{\prime \prime }-2 \left (a x +b \right ) y^{\prime }+\left (a^{2} x +2 a b \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.776 |
|
| \begin{align*}
x y^{\prime \prime }+\left (a x +b \right ) y^{\prime }+\left (c x +d \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
27.939 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x^{2}-x \right ) y^{\prime }+\left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.140 |
|
| \begin{align*}
x y^{\prime \prime }-\left (x^{2}-x -2\right ) y^{\prime }-x \left (x +3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.773 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 a \,x^{2}+1\right ) y^{\prime }+b \,x^{3} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.559 |
|
| \begin{align*}
x y^{\prime \prime }-2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
14.963 |
|
| \begin{align*}
x y^{\prime \prime }+\left (4 x^{2}-1\right ) y^{\prime }-4 x^{3} y-4 x^{5}&=0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.061 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.644 |
|
| \begin{align*}
x y^{\prime \prime }+\left (2 a x \ln \left (x \right )+1\right ) y^{\prime }+\left (a^{2} x \ln \left (x \right )^{2}+a \ln \left (x \right )+a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.647 |
|
| \begin{align*}
f \left (x \right ) y+\left (2+f \left (x \right ) x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.629 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.806 |
|
| \begin{align*}
a y+y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.855 |
|
| \begin{align*}
2 x y^{\prime \prime }-\left (x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
6.275 |
|
| \begin{align*}
2 x y^{\prime \prime }-\left (2 x -1\right ) y^{\prime }+a y&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
5.865 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.919 |
|
| \begin{align*}
4 x y^{\prime \prime }-\left (x +a \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.807 |
|