| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }+8 x y^{\prime \prime \prime }+12 y^{\prime \prime }-\lambda ^{2} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }+\left (2 n -2 \nu +4\right ) x y^{\prime \prime \prime }+\left (n -\nu +1\right ) \left (n -\nu +2\right ) y^{\prime \prime }-\frac {b^{4} y}{16}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime \prime }+2 x^{2} y^{\prime \prime \prime }-y^{\prime \prime } x +y^{\prime }-a^{4} x^{3} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.054 |
|
| \begin{align*}
6 y^{\prime \prime } x +6 x^{2} y^{\prime \prime \prime }+x^{3} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }-2 n \left (n +1\right ) x^{2} y^{\prime \prime }+4 n \left (n +1\right ) x y^{\prime }+\left (x^{4} a +n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.064 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }+\left (4 n^{2}-1\right ) x y^{\prime }-4 x^{4} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.107 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}-1\right ) x^{2} y^{\prime \prime }-\left (4 n^{2}-1\right ) x y^{\prime }+\left (-4 x^{4}+4 n^{2}-1\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.056 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+4 x^{3} y^{\prime \prime \prime }-\left (4 n^{2}+3\right ) x^{2} y^{\prime \prime }+\left (12 n^{2}-3\right ) x y^{\prime }-\left (4 x^{4}+12 n^{2}-3\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.064 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-\rho ^{2}-\sigma ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-\rho ^{2}-\sigma ^{2}+1\right ) x \right ) y^{\prime }+\left (\rho ^{2} \sigma ^{2}+8 x^{2}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.069 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+6 x^{3} y^{\prime \prime \prime }+\left (4 x^{4}+\left (-2 \mu ^{2}-2 \nu ^{2}+7\right ) x^{2}\right ) y^{\prime \prime }+\left (16 x^{3}+\left (-2 \mu ^{2}-2 \nu ^{2}+1\right ) x \right ) y^{\prime }+\left (8 x^{2}+\left (\mu ^{2}-\nu ^{2}\right )^{2}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.071 |
|
| \begin{align*}
12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
a y+12 x^{2} y^{\prime \prime }+8 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.192 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a \right ) x^{3} y^{\prime \prime \prime }+\left (4 x^{2 c} b^{2} c^{2}+6 \left (-1+a \right )^{2}-2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )+1\right ) x^{2} y^{\prime \prime }+\left (4 \left (3 c -2 a +1\right ) b^{2} c^{2} x^{2 c}+\left (2 a -1\right ) \left (2 c^{2} \left (\mu ^{2}+\nu ^{2}\right )-2 a \left (-1+a \right )-1\right )\right ) x y^{\prime }+\left (4 \left (a -c \right ) \left (a -2 c \right ) b^{2} c^{2} x^{2 c}+\left (c \mu +c \nu +a \right ) \left (c \mu +c \nu -a \right ) \left (c \mu -c \nu +a \right ) \left (c \mu -c \nu -a \right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.119 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+\left (6-4 a -4 c \right ) x^{3} y^{\prime \prime \prime }+\left (-2 \nu ^{2} c^{2}+2 a^{2}+4 \left (a +c -1\right )^{2}+4 \left (-1+a \right ) \left (c -1\right )-1\right ) x^{2} y^{\prime \prime }+\left (2 \nu ^{2} c^{2}-2 a^{2}-\left (2 a -1\right ) \left (2 c -1\right )\right ) \left (2 a +2 c -1\right ) x y^{\prime }+\left (\left (-\nu ^{2} c^{2}+a^{2}\right ) \left (-\nu ^{2} c^{2}+a^{2}+4 a c +4 c^{2}\right )-b^{4} c^{4} x^{4 c}\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.100 |
|
| \begin{align*}
\nu ^{4} x^{4} y^{\prime \prime \prime \prime }+\left (4 \nu -2\right ) \nu ^{3} x^{3} y^{\prime \prime \prime }+\left (\nu -1\right ) \left (2 \nu -1\right ) \nu ^{2} x^{2} y^{\prime \prime }-\frac {b^{4} x^{\frac {2}{\nu }} y}{16}&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.061 |
|
| \begin{align*}
\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (\nu +1\right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (\nu +1\right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (\nu +1\right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
0.078 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+2 x \right ) y^{\prime \prime \prime \prime }+4 \left ({\mathrm e}^{x}+2\right ) y^{\prime \prime \prime }+6 \,{\mathrm e}^{x} y^{\prime \prime }+4 \,{\mathrm e}^{x} y^{\prime }+{\mathrm e}^{x} y-\frac {1}{x^{5}}&=0 \\
\end{align*} |
[[_high_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| \begin{align*}
y^{\prime \prime \prime \prime } \sin \left (x \right )^{4}+2 y^{\prime \prime \prime } \sin \left (x \right )^{3} \cos \left (x \right )+y^{\prime \prime } \sin \left (x \right )^{2} \left (\sin \left (x \right )^{2}-3\right )+y^{\prime } \sin \left (x \right ) \cos \left (x \right ) \left (2 \sin \left (x \right )^{2}+3\right )+\left (a^{4} \sin \left (x \right )^{4}-3\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.115 |
|
| \begin{align*}
y^{\prime \prime \prime \prime } \sin \left (x \right )^{6}+4 y^{\prime \prime \prime } \sin \left (x \right )^{5} \cos \left (x \right )-6 y^{\prime \prime } \sin \left (x \right )^{6}-4 y^{\prime } \sin \left (x \right )^{5} \cos \left (x \right )+y \sin \left (x \right )^{6}-f&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
0.094 |
|
| \begin{align*}
f \left (y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y\right )+2 \operatorname {df} \left (y^{\prime \prime \prime }-a^{2} y^{\prime }\right )&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.089 |
|
| \begin{align*}
f y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.057 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 a^{2} y^{\prime \prime }+a^{4} y-\lambda \left (a x -b \right ) \left (y^{\prime \prime }-a^{2} y\right )&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.060 |
|
| \begin{align*}
y^{\left (5\right )}+2 y^{\prime \prime \prime }+y^{\prime }-a x -b \sin \left (x \right )-c \cos \left (x \right )&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.412 |
|
| \begin{align*}
y^{\left (6\right )}+y-\sin \left (\frac {3 x}{2}\right ) \sin \left (\frac {x}{2}\right )&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.496 |
|
| \begin{align*}
y^{\left (5\right )}-a x y-b&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.039 |
|
| \begin{align*}
y^{\left (5\right )}+a \,x^{\nu } y^{\prime }+a \nu \,x^{\nu -1} y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✓ |
✗ |
0.086 |
|
| \begin{align*}
y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.134 |
|
| \begin{align*}
x y^{\left (5\right )}-m n y^{\prime \prime \prime \prime }+a x y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| \begin{align*}
x \left (a y^{\prime }+b y^{\prime \prime }+c y^{\prime \prime \prime }+e y^{\prime \prime \prime \prime }\right ) y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.312 |
|
| \begin{align*}
x y^{\left (5\right )}-\left (a A_{1} -A_{0} \right ) x -A_{1} -\left (\left (a A_{2} -A_{1} \right ) x +A_{2} \right ) y^{\prime }&=0 \\
\end{align*} |
[[_high_order, _missing_y]] |
✗ |
✗ |
✗ |
✗ |
0.086 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \begin{align*}
x^{10} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| \begin{align*}
\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.064 |
|
| \begin{align*}
y^{\prime \prime }-y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
3.242 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.754 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}-x&=0 \\
\end{align*} |
[[_Painleve, ‘1st‘]] |
✗ |
✗ |
✗ |
✗ |
0.428 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.231 |
|
| \begin{align*}
y^{\prime \prime }+a y^{2}+b x +c&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.471 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{3}-y x +a&=0 \\
\end{align*} |
[[_Painleve, ‘2nd‘]] |
✗ |
✗ |
✗ |
✗ |
0.488 |
|
| \begin{align*}
y^{\prime \prime }-a y^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
2.878 |
|
| \begin{align*}
y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.508 |
|
| \begin{align*}
y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.527 |
|
| \begin{align*}
y^{\prime \prime }+d +b y^{2}+c y+a y^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
215.590 |
|
| \begin{align*}
y^{\prime \prime }+a \,x^{r} y^{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.449 |
|
| \begin{align*}
y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.283 |
|
| \begin{align*}
y^{\prime \prime }-\frac {1}{\left (a y^{2}+b x y+c \,x^{2}+\alpha y+\beta x +\gamma \right )^{{3}/{2}}}&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✗ |
✗ |
1.151 |
|
| \begin{align*}
y^{\prime \prime }-{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
7.086 |
|
| \begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.473 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.920 |
|
| \begin{align*}
a \sin \left (y\right )+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
43.859 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.432 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.112 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
22.408 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
10.487 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
606.358 |
|
| \begin{align*}
y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
498.497 |
|
| \begin{align*}
y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
14.662 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.450 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
25.837 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.536 |
|
| \begin{align*}
-y^{3}+y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
69.011 |
|
| \begin{align*}
y^{\prime \prime }+y y^{\prime }-y^{3}+a y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
194.312 |
|
| \begin{align*}
y^{\prime \prime }+\left (3 a +y\right ) y^{\prime }-y^{3}+a y^{2}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
32.642 |
|
| \begin{align*}
y^{\prime \prime }+\left (y+3 f \left (x \right )\right ) y^{\prime }-y^{3}+f \left (x \right ) y^{2}+y \left (2 f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.997 |
|
| \begin{align*}
y^{\prime \prime }+\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.895 |
|
| \begin{align*}
y^{\prime \prime }-3 y y^{\prime }-3 a y^{2}-4 a^{2} y-b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
34.242 |
|
| \begin{align*}
y^{\prime \prime }-\left (3 y+f \left (x \right )\right ) y^{\prime }+y^{3}+f \left (x \right ) y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_potential_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.813 |
|
| \begin{align*}
y^{\prime \prime }-2 a y y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.981 |
|
| \begin{align*}
y^{\prime \prime }+a y y^{\prime }+y^{3} b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
73.191 |
|
| \begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.251 |
|
| \begin{align*}
c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
36.358 |
|
| \begin{align*}
b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
5.862 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
11.680 |
|
| \begin{align*}
b y+a y {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.059 |
|
| \begin{align*}
a y \left (1+{y^{\prime }}^{2}\right )^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.198 |
|
| \begin{align*}
y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.244 |
|
| \begin{align*}
y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.748 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
4.450 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.064 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
447.299 |
|
| \begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
6.228 |
|
| \begin{align*}
y^{\prime \prime }-2 a x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✗ |
1.080 |
|
| \begin{align*}
y^{\prime \prime }-a y \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
7.835 |
|
| \begin{align*}
y^{\prime \prime }&=2 a \left (c +b x +y\right ) \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]] |
✗ |
✓ |
✓ |
✗ |
1.118 |
|
| \begin{align*}
y^{\prime \prime }+y^{3} y^{\prime }-y y^{\prime } \sqrt {y^{4}+4 y^{\prime }}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
157.724 |
|
| \begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-x y^{n}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.593 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a \,x^{v} y^{n}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.575 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+x \,{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.569 |
|
| \begin{align*}
b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.577 |
|
| \begin{align*}
y^{\prime \prime } x +a y^{\prime }+b \,x^{5-2 a} {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.866 |
|
| \begin{align*}
y^{\prime \prime } x +\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
0.943 |
|
| \begin{align*}
y^{\prime \prime } x -x^{2} {y^{\prime }}^{2}+2 y^{\prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.686 |
|
| \begin{align*}
y^{\prime \prime } x +a \left (-y+y^{\prime } x \right )^{2}-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.651 |
|
| \begin{align*}
y^{\prime }+{y^{\prime }}^{3}+2 y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.624 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.615 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (2 a +b -1\right ) x y^{\prime }+\left (c^{2} b^{2} x^{2 b}+a \left (a +b \right )\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.457 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a \left (-y+y^{\prime } x \right )^{2}-b \,x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.781 |
|