| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
16 y+8 y^{\prime }+y^{\prime \prime }&=4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.457 |
|
| \begin{align*}
20 y-9 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.173 |
|
| \begin{align*}
20 y-9 y^{\prime }+y^{\prime \prime }&=x^{2} {\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.321 |
|
| \begin{align*}
b^{2} y+2 a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
b^{2} y+2 a y^{\prime }+y^{\prime \prime }&=c \sin \left (k x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.590 |
|
| \begin{align*}
y^{\prime \prime }-2 a y^{\prime }+a^{2} y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.349 |
|
| \begin{align*}
\left (a^{2}+b^{2}\right )^{2} y-4 a b y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.331 |
|
| \begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
b y+a y^{\prime }+y^{\prime \prime }&=f \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.023 |
|
| \begin{align*}
\left (c x +b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.193 |
|
| \begin{align*}
\left (c \,x^{2}+b \right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.783 |
|
| \begin{align*}
\left (b +c \,{\mathrm e}^{x}\right ) y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.184 |
|
| \begin{align*}
b \,{\mathrm e}^{2 a x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.208 |
|
| \begin{align*}
b \,{\mathrm e}^{k x} y+a y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.209 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| \begin{align*}
2 y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} | [_Hermite] | ✓ | ✓ | ✓ | ✗ | 0.478 |
|
| \begin{align*}
n y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✗ |
✓ |
✓ |
✗ |
1.418 |
|
| \begin{align*}
-a y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_Hermite] |
✗ |
✓ |
✓ |
✗ |
1.163 |
|
| \begin{align*}
-\left (1-x \right ) y-y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.327 |
|
| \begin{align*}
6 y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.490 |
|
| \begin{align*}
-8 y+2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[_erf] |
✓ |
✓ |
✓ |
✗ |
0.448 |
|
| \begin{align*}
2 n y-2 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.418 |
|
| \begin{align*}
-\left (-x^{2}-x +1\right ) y-\left (2 x +1\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.355 |
|
| \begin{align*}
2 \left (2 x^{2}+1\right ) y+4 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.322 |
|
| \begin{align*}
-\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.317 |
|
| \begin{align*}
-\left (-4 x^{2}+3\right ) y-4 y^{\prime } x +y^{\prime \prime }&={\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| \begin{align*}
y a^{2} x^{2}-2 a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| \begin{align*}
b y+a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.540 |
|
| \begin{align*}
c y+\left (b x +a \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.734 |
|
| \begin{align*}
\left (\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.223 |
|
| \begin{align*}
\left (\operatorname {c1} \,x^{2}+\operatorname {b1} x +\operatorname {a1} \right ) y+\left (\operatorname {b0} x +\operatorname {a0} \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.904 |
|
| \begin{align*}
-2 a \left (-2 a \,x^{2}+1\right ) y-4 a x y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.379 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.449 |
|
| \begin{align*}
-4 y x +x^{2} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✓ | ✓ | ✓ | ✗ | 0.638 |
|
| \begin{align*}
-x^{3} y+x^{4} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.173 |
|
| \begin{align*}
a \left (1+k \right ) x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
1.591 |
|
| \begin{align*}
a k \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
0.565 |
|
| \begin{align*}
-a \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.563 |
|
| \begin{align*}
b \,x^{-1+k} y+a \,x^{k} y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.587 |
|
| \begin{align*}
2 y-\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.835 |
|
| \begin{align*}
k \left (1+k \right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
1.436 |
|
| \begin{align*}
-\csc \left (x \right )^{2} y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.743 |
|
| \begin{align*}
\left (p \left (1+p \right )-k^{2} \csc \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.551 |
|
| \begin{align*}
\left (\operatorname {a0} -\operatorname {a2} \csc \left (x \right )^{2}+4 \operatorname {a1} \sin \left (x \right )^{2}\right ) y+\cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
5.468 |
|
| \begin{align*}
3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.688 |
|
| \begin{align*}
3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.612 |
|
| \begin{align*}
\left (b +k^{2} \cos \left (x \right )^{2}\right ) y+a \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
3.953 |
|
| \begin{align*}
\left (a \cot \left (x \right )^{2}+b \cot \left (x \right ) \csc \left (x \right )+c \csc \left (x \right )^{2}\right ) y+k \cot \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
3.696 |
|
| \begin{align*}
2 y-\cot \left (2 x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.015 |
|
| \begin{align*}
a \tan \left (x \right )^{2} y-2 \cot \left (2 x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.492 |
|
| \begin{align*}
c y+a \cot \left (b x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
13.372 |
|
| \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]] | ✓ | ✓ | ✓ | ✗ | 0.476 |
|
| \begin{align*}
a \tan \left (\frac {x}{2}\right )^{2} y-\csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✗ |
✓ |
✗ |
6.579 |
|
| \begin{align*}
\left (\csc \left (x \right )+\cot \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=1+a \csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
2.541 |
|
| \begin{align*}
\csc \left (x \right )^{2} \left (2+\sin \left (x \right )^{2}\right ) y-\csc \left (2 x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
82.041 |
|
| \begin{align*}
a \csc \left (x \right )^{2} y+\left (2+\cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.406 |
|
| \begin{align*}
-2 \left (\cos \left (x \right )+1\right ) \sec \left (x \right ) y-\left (2+3 \cos \left (x \right )\right ) \csc \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.812 |
|
| \begin{align*}
y \sin \left (x \right )^{2}-\left (\cot \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.987 |
|
| \begin{align*}
-y \cos \left (x \right )-\sin \left (x \right ) y^{\prime }+y^{\prime \prime }&=a -x +x \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.727 |
|
| \begin{align*}
b \tan \left (x \right )^{2} y-2 \csc \left (2 x \right ) \left (1-a \sin \left (x \right )^{2}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.636 |
|
| \begin{align*}
a \cos \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.582 |
|
| \begin{align*}
a \cot \left (x \right )^{2} y+\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.536 |
|
| \begin{align*}
-a \left (a +1\right ) \csc \left (x \right )^{2} y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.611 |
|
| \begin{align*}
\left (a \cos \left (x \right )^{2}-\sec \left (x \right )^{2}\right ) y-\tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.530 |
|
| \begin{align*}
-y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.016 |
|
| \begin{align*}
-y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=\left (x +1\right ) \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
147.852 |
|
| \begin{align*}
3 y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.909 |
|
| \begin{align*}
b y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.542 |
|
| \begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.483 |
|
| \begin{align*}
-\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.760 |
|
| \begin{align*}
b y+a \tan \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} | [[_2nd_order, _with_linear_symmetries]] | ✗ | ✓ | ✓ | ✗ | 2.105 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x}-\left (1+2 \,{\mathrm e}^{x}\right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.859 |
|
| \begin{align*}
\left (\operatorname {a0} -\operatorname {a2} \operatorname {csch}\left (x \right )^{2}+4 \operatorname {a1} \sinh \left (x \right )^{2}\right ) y+\coth \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
36.720 |
|
| \begin{align*}
\left (\operatorname {a0} +4 \operatorname {a1} \cosh \left (x \right )^{2}-\operatorname {a2} \operatorname {sech}\left (x \right )^{2}\right ) y+\tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
31.491 |
|
| \begin{align*}
b y+2 \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.697 |
|
| \begin{align*}
b y+a \tanh \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
9.916 |
|
| \begin{align*}
f \left (x \right ) y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
a k \,x^{-1+k} y+2 a \,x^{k} y^{\prime }+2 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
2.161 |
|
| \begin{align*}
3 y-10 y^{\prime }+3 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.184 |
|
| \begin{align*}
4 y^{\prime \prime }&=\left (x^{2}+a \right ) y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.950 |
|
| \begin{align*}
\left (-x^{2}+4 a +2\right ) y+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.955 |
|
| \begin{align*}
3 y-8 y^{\prime }+4 y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.181 |
|
| \begin{align*}
y^{\prime \prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \begin{align*}
\left (x +a \right ) y+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.849 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.726 |
|
| \begin{align*}
y^{\prime \prime } x +y^{\prime }&=x^{n} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.165 |
|
| \begin{align*}
-y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.222 |
|
| \begin{align*}
-\left (x +1\right ) y+y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.375 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.290 |
|
| \begin{align*}
-a^{2} x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} | [[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] | ✓ | ✓ | ✓ | ✓ | 1.257 |
|
| \begin{align*}
\left ({\mathrm e}^{x^{2}}-k^{2}\right ) x^{3} y-y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
4.554 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.592 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.572 |
|
| \begin{align*}
y^{\prime \prime } x +2 y^{\prime }-y x&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.889 |
|
| \begin{align*}
a x y+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.498 |
|
| \begin{align*}
a \,x^{2} y+2 y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
a y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.839 |
|