| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
43.168 |
|
| \begin{align*}
4 y-\left (x +4\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
46.201 |
|
| \begin{align*}
-2 y+2 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
79.551 |
|
| \begin{align*}
6 y+\left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
47.861 |
|
| \begin{align*}
p \left (1+p \right ) y+\left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
87.218 |
|
| \begin{align*}
2 y+\left (1-x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
50.379 |
|
| \begin{align*}
-y-3 y^{\prime } x +\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
105.003 |
|
| \begin{align*}
y+\left (3 x +2\right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
29.369 |
|
| \begin{align*}
-2 y+\left (1-4 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
29.170 |
|
| \begin{align*}
-2 y-2 \left (2 x +1\right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
28.970 |
|
| \begin{align*}
-6 y-2 \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
49.671 |
|
| \begin{align*}
\left (-k +p \right ) \left (1+k +p \right ) y+\left (1+k \right ) \left (1-2 x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
140.238 |
|
| \begin{align*}
n \left (a +n \right ) y+\left (c -\left (1+a \right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
155.986 |
|
| \begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
103.810 |
|
| \begin{align*}
-a b y+\left (c -\left (a +b +1\right ) x \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
198.063 |
|
| \begin{align*}
-a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
89.214 |
|
| \begin{align*}
-a y-\left (a -\left (2-a \right ) x \right ) y^{\prime }+x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
61.300 |
|
| \begin{align*}
c y+\left (b x +a \right ) y^{\prime }+\left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
165.549 |
|
| \begin{align*}
x \left (7+6 x \right ) y+x \left (1-x \right ) y^{\prime }+\left (-x^{2}-x +2\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
39.935 |
|
| \begin{align*}
2 y+2 \left (1-x \right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
27.320 |
|
| \begin{align*}
2 \left (1-x \right ) y-\left (-x^{2}+2\right ) y^{\prime }+\left (-x +2\right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
59.747 |
|
| \begin{align*}
2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
62.088 |
|
| \begin{align*}
2 y-4 \left (1-x \right ) y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
53.162 |
|
| \begin{align*}
6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
32.197 |
|
| \begin{align*}
6 y-4 \left (x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
20.578 |
|
| \begin{align*}
-\left (2+x \right ) y-\left (-x^{2}-x +1\right ) y^{\prime }+\left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
44.968 |
|
| \begin{align*}
\left (1-x \right )^{2} y-2 \left (1-x \right )^{2} y^{\prime }+\left (1-x \right )^{2} y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
86.344 |
|
| \begin{align*}
-\left (2 x +3\right ) y+\left (x^{2}+x +1\right ) y^{\prime }+\left (x^{2}+3 x +4\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
53.710 |
|
| \begin{align*}
2 y-\left (2+x \right ) y^{\prime }+\left (2+x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
33.069 |
|
| \begin{align*}
-3 y+\left (-x +2\right ) y^{\prime }+\left (-x +2\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
59.918 |
|
| \begin{align*}
\operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x \left (\operatorname {a0} +x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
112.040 |
|
| \begin{align*}
6 y-4 \left (a +x \right ) y^{\prime }+\left (\operatorname {a0} +x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
101.333 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.293 |
|
| \begin{align*}
-3 y+y^{\prime } x +2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.586 |
|
| \begin{align*}
2 \left (x +5\right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
13.039 |
|
| \begin{align*}
-2 \left (1-3 x \right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
13.148 |
|
| \begin{align*}
-2 \left (1-3 x \right ) y-x \left (1-4 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=x^{3} \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
6.589 |
|
| \begin{align*}
-3 y+3 y^{\prime } x +\left (2 x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
24.236 |
|
| \begin{align*}
2 a^{2} y-y^{\prime } x +2 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
74.990 |
|
| \begin{align*}
-4 y+y^{\prime }+2 x \left (x +1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.420 |
|
| \begin{align*}
-y+\left (x +1\right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
47.359 |
|
| \begin{align*}
y+\left (1-x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✓ |
✓ |
✓ |
✗ |
49.943 |
|
| \begin{align*}
-2 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
16.005 |
|
| \begin{align*}
8 y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
18.256 |
|
| \begin{align*}
a y-\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
68.302 |
|
| \begin{align*}
\left (b x +a \right ) y+\left (1-2 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
95.447 |
|
| \begin{align*}
2 a \left (1+a \right ) y-\left (1+3 x \right ) y^{\prime }+2 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
109.748 |
|
| \begin{align*}
4 y+2 \left (1-2 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
65.350 |
|
| \begin{align*}
12 y+2 \left (3-4 x \right ) y^{\prime }+\left (1-2 x \right ) \left (1-x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
34.533 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
35.576 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+2 \left (x +1\right )^{2} y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
25.424 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.617 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+y&=\sqrt {x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.550 |
|
| \begin{align*}
\left (4 x k -4 p^{2}-x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.818 |
|
| \begin{align*}
\left (4 a^{2} x^{2}+1\right ) y+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.444 |
|
| \begin{align*}
-\left (a^{2}-x \right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.050 |
|
| \begin{align*}
-\left (4 x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=4 x^{{3}/{2}} {\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
63.414 |
|
| \begin{align*}
-\left (\left (2 n +1\right )^{2}-4 x^{2}\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
66.010 |
|
| \begin{align*}
-\left (a^{2} x^{2}+1\right ) y+4 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.144 |
|
| \begin{align*}
5 y-8 y^{\prime } x +4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.018 |
|
| \begin{align*}
\left (x +3\right ) y-2 x \left (2+x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
14.572 |
|
| \begin{align*}
-\left (-4 x^{2}+4 x +1\right ) y+4 x \left (1-2 x \right ) y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
14.099 |
|
| \begin{align*}
-\left (-2 x^{2}+3\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
9.346 |
|
| \begin{align*}
\left (x^{4}+2 x^{2}+1\right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.417 |
|
| \begin{align*}
\left (x^{4}+2 x^{2}+a \right ) y+4 x^{3} y^{\prime }+4 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.151 |
|
| \begin{align*}
-y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
36.243 |
|
| \begin{align*}
-\left (4 p^{2}+1\right ) y-8 y^{\prime } x +4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
57.059 |
|
| \begin{align*}
4 \left (x^{2}+1\right ) y^{\prime \prime }&=x^{2}+4 y^{\prime } x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.661 |
|
| \begin{align*}
-a \left (2+a \right ) y+4 a x y^{\prime }+4 \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
104.692 |
|
| \begin{align*}
y+2 \left (1-x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
47.480 |
|
| \begin{align*}
\left (b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✗ |
✗ |
113.355 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right ) y+2 \left (1-2 x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
133.726 |
|
| \begin{align*}
-\left (k -p \right ) \left (1+k +p \right ) y+2 \left (1-\left (3-2 k \right ) x \right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✓ |
✗ |
144.792 |
|
| \begin{align*}
\left (k^{2} x +b \right ) y+2 \left (a x +1\right ) y^{\prime }+4 \left (1-x \right ) x y^{\prime \prime }&=0 \\
\end{align*} |
[_Jacobi] |
✗ |
✓ |
✗ |
✗ |
106.692 |
|
| \begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
36.292 |
|
| \begin{align*}
-12 y-2 \left (2 x +1\right ) y^{\prime }+\left (2 x +1\right )^{2} y^{\prime \prime }&=1+3 x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
23.831 |
|
| \begin{align*}
-9 y-3 \left (1-3 x \right ) y^{\prime }+\left (1-3 x \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
165.799 |
|
| \begin{align*}
\left (4 x +3\right ) y+16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.953 |
|
| \begin{align*}
-\left (5+4 x \right ) y+32 y^{\prime } x +16 x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.382 |
|
| \begin{align*}
b^{2} y+a x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
181.865 |
|
| \begin{align*}
c y+b x y^{\prime }+\left (a \,x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
576.561 |
|
| \begin{align*}
-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
3.039 |
|
| \begin{align*}
2 a^{2} y-2 a^{2} x y^{\prime }+\left (-a^{2} x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[_Gegenbauer] |
✓ |
✓ |
✓ |
✓ |
34.648 |
|
| \begin{align*}
-2 b y+2 a y^{\prime }+x \left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
30.237 |
|
| \begin{align*}
2 \operatorname {a2} y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {c0} \,x^{2}+\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
266.234 |
|
| \begin{align*}
\operatorname {a2} y+\operatorname {a1} \left (b x +a \right ) y^{\prime }+\left (b x +a \right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
262.527 |
|
| \begin{align*}
x^{3} y^{\prime \prime }&=b x +a \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.811 |
|
| \begin{align*}
-y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
15.983 |
|
| \begin{align*}
-2 y+y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
8.575 |
|
| \begin{align*}
-y+2 y^{\prime } x +x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
16.069 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\operatorname {a1} x y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
18.591 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
32.401 |
|
| \begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
20.132 |
|
| \begin{align*}
y x +3 x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.786 |
|
| \begin{align*}
\left (c x +b \right ) y+a \,x^{2} y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
24.626 |
|
| \begin{align*}
\operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
107.535 |
|
| \begin{align*}
\operatorname {a2} y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
118.694 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+x \left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
126.292 |
|
| \begin{align*}
6 y x +\left (-x^{3}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.508 |
|
| \begin{align*}
-y^{\prime }+x \left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.929 |
|