| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
11.871 |
|
| \begin{align*}
y+\left (1-a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
10.741 |
|
| \begin{align*}
-y+\left (a +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✓ |
✓ |
✗ |
7.912 |
|
| \begin{align*}
-y+2 n y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.385 |
|
| \begin{align*}
b y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.246 |
|
| \begin{align*}
b x y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.381 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {b1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
12.941 |
|
| \begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
10.646 |
|
| \begin{align*}
b \,x^{k} y+a y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✗ |
1.174 |
|
| \begin{align*}
y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
2.030 |
|
| \begin{align*}
n y+\left (1-x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
12.221 |
|
| \begin{align*}
n y+\left (1+k -x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
37.666 |
|
| \begin{align*}
2 \left (1-x \right ) y-\left (x +1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.520 |
|
| \begin{align*}
-y-\left (2-x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.548 |
|
| \begin{align*}
y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
2.097 |
|
| \begin{align*}
3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.443 |
|
| \begin{align*}
b y+\left (x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
12.780 |
|
| \begin{align*}
-a y+\left (c -x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✗ |
✓ |
✓ |
✗ |
12.783 |
|
| \begin{align*}
-\left (1-x \right ) y+\left (1-2 x \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.771 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.828 |
|
| \begin{align*}
x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y&=x^{2}-x -1 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| \begin{align*}
c y+\left (b x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
31.944 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
15.138 |
|
| \begin{align*}
\left (b x +2 a \right ) y-2 \left (b x +a \right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
39.273 |
|
| \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]] |
✗ |
✓ |
✓ |
✗ |
18.211 |
|
| \begin{align*}
-\left (-x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| \begin{align*}
2 y x -\left (-x^{2}+4\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.069 |
|
| \begin{align*}
x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.008 |
|
| \begin{align*}
-8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.447 |
|
| \begin{align*}
-8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=4 x^{3} {\mathrm e}^{-x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.959 |
|
| \begin{align*}
4 x \left (x^{2}+1\right ) y+\left (4 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| \begin{align*}
a \,x^{2} \left (a \,x^{3}+1\right ) y-\left (-2 a \,x^{3}+1\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.251 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.216 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.899 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+x y^{\prime }-y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.109 |
|
| \begin{align*}
3 \left (2-x \right ) y-\left (9-4 x \right ) y^{\prime }+\left (-x +3\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.634 |
|
| \begin{align*}
-2 y^{\prime }+\left (-x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
33.888 |
|
| \begin{align*}
y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.858 |
|
| \begin{align*}
a y+y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.315 |
|
| \begin{align*}
-a y+y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.561 |
|
| \begin{align*}
\left (b x +a \right ) y+y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
17.651 |
|
| \begin{align*}
-y x -\left (2 x^{2}+1\right ) y^{\prime }+2 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.266 |
|
| \begin{align*}
-y-\left (x +2\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.109 |
|
| \begin{align*}
\left (-x +3\right ) y-\left (-3 x +4\right ) y^{\prime }+\left (1-2 x \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.879 |
|
| \begin{align*}
y+2 y^{\prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
-y-2 y^{\prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.626 |
|
| \begin{align*}
y+4 \coth \left (x \right ) y^{\prime }+4 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✗ |
✗ |
✗ |
✗ |
75.662 |
|
| \begin{align*}
\left (b x +a \right ) y+8 y^{\prime }+16 x y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
10.405 |
|
| \begin{align*}
c y^{\prime }+\left (b x +a \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.960 |
|
| \begin{align*}
\left (\operatorname {b2} x +\operatorname {a2} \right ) y+\left (\operatorname {b1} x +\operatorname {a1} \right ) y^{\prime }+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
39.799 |
|
| \begin{align*}
y-x y^{\prime }+\left (-x \cot \left (x \right )+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.387 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=b x +a \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.664 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=2 y \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.322 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=6 y \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=12 y \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
a y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.065 |
|
| \begin{align*}
\left (b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.744 |
|
| \begin{align*}
-\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
-\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=x^{4} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.505 |
|
| \begin{align*}
-\left (a^{2} x^{2}+2\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.455 |
|
| \begin{align*}
-\left (-a^{2} x^{2}+6\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.513 |
|
| \begin{align*}
-\left (n \left (n +1\right )+a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.426 |
|
| \begin{align*}
-\left (\left (n -1\right ) n -a^{2} x^{2}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.999 |
|
| \begin{align*}
\left (c \,x^{2}+b x +a \right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
7.893 |
|
| \begin{align*}
-\left (\left (a -1\right ) a -b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.859 |
|
| \begin{align*}
x^{k} \left (a +b \,x^{k}\right ) y+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.316 |
|
| \begin{align*}
-b \left (b \,x^{2}+a \right ) y+a y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.661 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.867 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
4.104 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }-y&=a \,x^{2} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
5.549 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=x^{2} \left (x +3\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.690 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=3 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.468 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+x y^{\prime }+y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
18.761 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
5.003 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+2 y&=x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
52.994 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.900 |
|
| \begin{align*}
-a^{2} y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| \begin{align*}
\left (b x +a \right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.151 |
|
| \begin{align*}
-\left (p^{2}-x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[_Bessel] |
✓ |
✓ |
✓ |
✓ |
2.738 |
|
| \begin{align*}
-\left (p^{2}+x^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_Bessel, _modified]] |
✓ |
✓ |
✓ |
✓ |
2.175 |
|
| \begin{align*}
-\left (i x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.294 |
|
| \begin{align*}
-\left (-a^{2} x^{2}+p^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.460 |
|
| \begin{align*}
-\left (c \,x^{2}+b x +a \right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
41.661 |
|
| \begin{align*}
-\left (-x^{4}+4 a \,x^{2}+n^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
141.732 |
|
| \begin{align*}
-\left (c^{2} x^{4}+b^{2} x^{2}+a^{2}\right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
33.327 |
|
| \begin{align*}
\left (m +1\right ) x^{m} a \left (m \right ) y+x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✓ |
29.606 |
|
| \begin{align*}
-y+\left (x +a \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.783 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
6.052 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=4 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.009 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{3} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
39.598 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=2 x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
38.697 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y&=x^{5} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
38.556 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.122 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-6 y&=2-x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.620 |
|
| \begin{align*}
\left (a^{2} x^{2}+2\right ) y-2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.225 |
|
| \begin{align*}
-\left (n \left (n +1\right )-a^{2} x^{2}\right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.622 |
|
| \begin{align*}
\left (b \,x^{2}+a \right ) y+2 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.523 |
|
| \begin{align*}
a y-2 \left (1-x \right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
37.306 |
|