| # |
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]] |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.048 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.045 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.228 |
|
| \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 (a \,x^{4}+n \left (n +1\right ) \left (n +3\right ) \left (-2+n \right )\right ) y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.051 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.091 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.049 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.052 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.057 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.105 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.134 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.095 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.082 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.058 |
|
| \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]] |
✗ |
✓ |
✗ |
✗ |
0.063 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.260 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.088 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.070 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.064 |
|
| \begin{align*}
f y^{\prime \prime \prime \prime }&=0 \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.033 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.050 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
1.060 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.289 |
|
| \begin{align*}
y^{\left (5\right )}-a x y-b&=0 \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✗ |
✗ |
✗ |
✗ |
0.034 |
|
| \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]] |
✗ |
✗ |
✓ |
✗ |
0.073 |
|
| \begin{align*}
y^{\left (5\right )}+a y^{\prime \prime \prime \prime }-f&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.101 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.212 |
|
| \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]] |
✗ |
✗ |
✗ |
✗ |
0.083 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime \prime }-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.034 |
|
| \begin{align*}
x^{10} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.037 |
|
| \begin{align*}
x^{{5}/{2}} y^{\left (5\right )}-a y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.043 |
|
| \begin{align*}
\left (x -a \right )^{5} \left (-b +x \right )^{5} y^{\left (5\right )}-c y&=0 \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.050 |
|
| \begin{align*}
y^{\prime \prime }-y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.676 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.439 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}-x&=0 \\
\end{align*} |
[[_Painleve, ‘1st‘]] |
✗ |
✗ |
✗ |
✗ |
0.337 |
|
| \begin{align*}
y^{\prime \prime }-6 y^{2}+4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.333 |
|
| \begin{align*}
y^{\prime \prime }+a y^{2}+b x +c&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.380 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{3}-y x +a&=0 \\
\end{align*} |
[[_Painleve, ‘2nd‘]] |
✗ |
✗ |
✗ |
✗ |
0.370 |
|
| \begin{align*}
y^{\prime \prime }-a y^{3}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
1.608 |
|
| \begin{align*}
y^{\prime \prime }-2 a^{2} y^{3}+2 a b x y-b&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.400 |
|
| \begin{align*}
y^{\prime \prime }+d +b x y+c y+a y^{3}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.423 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
185.215 |
|
| \begin{align*}
y^{\prime \prime }+a \,x^{r} y^{2}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.358 |
|
| \begin{align*}
y^{\prime \prime }+6 a^{10} y^{11}-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.344 |
|
| \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] |
✗ |
✓ |
✗ |
✗ |
0.953 |
|
| \begin{align*}
y^{\prime \prime }-{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
3.787 |
|
| \begin{align*}
y^{\prime \prime }+a \,{\mathrm e}^{x} \sqrt {y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.371 |
|
| \begin{align*}
y^{\prime \prime }+{\mathrm e}^{x} \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.707 |
|
| \begin{align*}
a \sin \left (y\right )+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
32.821 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta \sin \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.256 |
|
| \begin{align*}
y^{\prime \prime }+a^{2} \sin \left (y\right )-\beta f \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.908 |
|
| \begin{align*}
y^{\prime \prime }&=\frac {f \left (\frac {y}{\sqrt {x}}\right )}{x^{{3}/{2}}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
16.475 |
|
| \begin{align*}
y^{\prime \prime }-3 y^{\prime }-y^{2}-2 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
8.794 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }-y^{{3}/{2}}+12 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
106.090 |
|
| \begin{align*}
y^{\prime \prime }+5 a y^{\prime }-6 y^{2}+6 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
90.819 |
|
| \begin{align*}
y^{\prime \prime }+3 a y^{\prime }-2 y^{3}+2 a^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
11.780 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,x^{v} y^{n}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
0.402 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+b \,{\mathrm e}^{y}-2 a&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
21.361 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime }+f \left (x \right ) \sin \left (y\right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.008 |
|
| \begin{align*}
-y^{3}+y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
31.650 |
|
| \begin{align*}
y^{\prime \prime }+y y^{\prime }-y^{3}+a y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✗ |
✗ |
274.637 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
42.721 |
|
| \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] |
✗ |
✗ |
✗ |
✗ |
1.259 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
1.181 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
51.638 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
1.316 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.578 |
|
| \begin{align*}
y^{\prime \prime }+a y y^{\prime }+y^{3} b&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
59.927 |
|
| \begin{align*}
b y+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.957 |
|
| \begin{align*}
c y+b y^{\prime }+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
44.335 |
|
| \begin{align*}
b \sin \left (y\right )+a {y^{\prime }}^{2}+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.631 |
|
| \begin{align*}
y^{\prime \prime }+a y^{\prime } {| y^{\prime }|}+b \sin \left (y\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✗ |
✗ |
✗ |
19.865 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.251 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.362 |
|
| \begin{align*}
y^{\prime \prime }-a \left (-y+y^{\prime } x \right )^{v}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.954 |
|
| \begin{align*}
y^{\prime \prime }-k \,x^{a} y^{b} {y^{\prime }}^{r}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.636 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
2.589 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {1+{y^{\prime }}^{2}}+b \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
0.615 |
|
| \begin{align*}
y^{\prime \prime }&=a \sqrt {b y^{2}+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✗ |
✓ |
✓ |
✗ |
1039.573 |
|
| \begin{align*}
y^{\prime \prime }&=a \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
3.536 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.801 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
4.026 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
1.106 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
147.257 |
|
| \begin{align*}
9 {y^{\prime }}^{4}+8 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.966 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-x y^{n}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.663 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+a \,x^{v} y^{n}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.665 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }+x \,{\mathrm e}^{y}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.657 |
|
| \begin{align*}
b \,{\mathrm e}^{y} x +a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.676 |
|
| \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]] |
✗ |
✗ |
✗ |
✗ |
0.885 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.711 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.707 |
|
| \begin{align*}
y^{\prime \prime } x +a \left (-y+y^{\prime } x \right )^{2}-b&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.727 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
0.675 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=a \left (y^{n}-y\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.531 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+a \left ({\mathrm e}^{y}-1\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
0.572 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.343 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
0.852 |
|