| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y y^{\prime \prime }+\sqrt {{y^{\prime }}^{2}+a^{2} {y^{\prime \prime }}^{2}}&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
59.983 |
|
| \begin{align*}
\left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 y^{\prime } x +6 y&=6 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.365 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.762 |
|
| \begin{align*}
3 y-\left (x +3\right ) y^{\prime }+y^{\prime \prime } x&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
3.857 |
|
| \begin{align*}
y^{\prime \prime } x +\left (1-x \right ) y^{\prime }&={\mathrm e}^{x}+y \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.386 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }-2 \left (x +3\right ) y^{\prime }+\left (x +5\right ) y&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
8.792 |
|
| \begin{align*}
\left (-x +3\right ) y^{\prime \prime }-\left (9-4 x \right ) y^{\prime }+\left (6-3 x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.279 |
|
| \begin{align*}
-y+y^{\prime } x +y^{\prime \prime }&=X \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.271 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime \prime } x -y^{\prime }+y x&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.040 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_3rd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.159 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (2+x \right ) y&={\mathrm e}^{x} x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.276 |
|
| \begin{align*}
y^{\prime \prime }-a x y^{\prime }+a^{2} \left (x -1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.200 |
|
| \begin{align*}
\left (2 x^{3}-a \right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.131 |
|
| \begin{align*}
y^{\prime \prime }+4 y^{\prime } x +4 x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.455 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+n^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.436 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}&=n^{2} y \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
8.417 |
|
| \begin{align*}
y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.892 |
|
| \begin{align*}
y^{\prime \prime }-2 b x y^{\prime }+b^{2} x^{2} y&=x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.606 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✗ |
✗ |
✗ |
8.868 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{2}+x \right ) y^{\prime }+\left (4 x^{2}-2 x +1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
21.374 |
|
| \begin{align*}
y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&={\mathrm e}^{x} \sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
18.078 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.457 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.475 |
|
| \begin{align*}
y^{\prime \prime }+2 n \cot \left (x n \right ) y^{\prime }+\left (m^{2}-n^{2}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.647 |
|
| \begin{align*}
y^{\prime \prime }-\frac {y^{\prime }}{\sqrt {x}}+\frac {\left (x +\sqrt {x}-8\right ) y}{4 x^{2}}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.664 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 n x y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.572 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime } x +\left (4 x^{2}-3\right ) y&={\mathrm e}^{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.719 |
|
| \begin{align*}
y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+y \cos \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.121 |
|
| \begin{align*}
y^{\prime \prime }+\frac {2 y^{\prime }}{x}+\frac {a^{2} y}{x^{4}}&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
36.987 |
|
| \begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime }+y^{\prime }+n^{2} x^{3} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
78.960 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +m^{2} y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.214 |
|
| \begin{align*}
y^{\prime \prime }-\cot \left (x \right ) y^{\prime }-y \sin \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.996 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }+\cos \left (x \right ) \sin \left (x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.425 |
|
| \begin{align*}
4 y+2 x \left (x^{2}+1\right ) y^{\prime }+\left (x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
6.733 |
|
| \begin{align*}
y^{\prime \prime }+\left (\tan \left (x \right )-1\right )^{2} y^{\prime }-n \left (n -1\right ) y \sec \left (x \right )^{4}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.040 |
|
| \begin{align*}
y^{\prime \prime }+\left (3 \sin \left (x \right )-\cot \left (x \right )\right ) y^{\prime }+2 y \sin \left (x \right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.540 |
|
| \begin{align*}
3 x^{2} y^{\prime \prime }+\left (-6 x^{2}+2\right ) y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.615 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x -2\right ) y^{\prime }-2 y&=x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.194 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime }-\left (x^{2}+1\right ) y&={\mathrm e}^{-x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
8.188 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
10.053 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.336 |
|
| \begin{align*}
y^{\prime \prime }+y&=\csc \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
4.079 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=4 \tan \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.976 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }+y^{\prime } x -y&=\left (1-x \right )^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
9.562 |
|
| \begin{align*}
y^{\prime \prime }-y&=\frac {2}{{\mathrm e}^{x}+1} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
22.379 |
|
| \begin{align*}
-\left (x^{2}+1\right ) y-4 y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
39.897 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=-4 x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
6.196 |
|
| \begin{align*}
-y+y^{\prime } x&=\left (x -1\right ) \left (y^{\prime \prime }-x +1\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.629 |
|
| \begin{align*}
\left (-y+y^{\prime } x \right )^{2}+x^{2} y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.379 |
|
| \begin{align*}
2 \left (x +1\right ) y-2 x \left (x +1\right ) y^{\prime }+x^{2} y^{\prime \prime }&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.306 |
|
| \begin{align*}
\left (x^{2}+a \right ) y^{\prime \prime }-2 y^{\prime } x +2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
36.234 |
|
| \begin{align*}
y^{\prime \prime }-\frac {2 y^{\prime }}{x}+\left (n^{2}+\frac {2}{x^{2}}\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.720 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+1\right ) y&=x^{3}+3 x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.766 |
|
| \begin{align*}
\left (a^{2}-x^{2}\right ) y^{\prime \prime }-\frac {a^{2} y^{\prime }}{x}+\frac {x^{2} y}{a}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
9.949 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} y^{\prime }+n^{2} y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.967 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +\frac {a^{2} y}{-x^{2}+1}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
88.102 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime \prime }-2 y^{\prime }+\left (3-2 x \right ) y&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
11.546 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=8 x^{3} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.834 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime } x +\left (x^{2}+5\right ) y&=x \,{\mathrm e}^{-\frac {x^{2}}{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.282 |
|
| \begin{align*}
x \left (-x^{2}+1\right )^{2} y^{\prime \prime }+\left (-x^{2}+1\right ) \left (3 x^{2}+1\right ) y^{\prime }+4 x \left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
166.705 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\frac {2}{x^{2}}\right ) y&=x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.628 |
|
| \begin{align*}
\left (x^{3}-2 x^{2}\right ) y^{\prime \prime }+2 x^{2} y^{\prime }-12 \left (x -2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
101.343 |
|
| \begin{align*}
y^{\prime \prime } x -2 \left (x +1\right ) y^{\prime }+\left (2+x \right ) y&=\left (x -2\right ) {\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.077 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x -9 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.120 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -a^{2} y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
32.329 |
|
| \begin{align*}
x y^{\prime \prime } \left (\cos \left (x \right ) x -2 \sin \left (x \right )\right )+\left (x^{2}+2\right ) y^{\prime } \sin \left (x \right )-2 y \left (x \sin \left (x \right )+\cos \left (x \right )\right )&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✗ |
✗ |
0.217 |
|
| \begin{align*}
y^{\prime \prime } x -y^{\prime }+4 x^{3} y&=x^{5} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
7.041 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }-\left (4 x^{2}-3 x -5\right ) y^{\prime }+\left (4 x^{2}-6 x -5\right ) y&={\mathrm e}^{2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
175.077 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x&=m^{2} y \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
7.246 |
|
| \begin{align*}
y^{\prime \prime }+\left (1-\frac {1}{x}\right ) y^{\prime }+4 x^{2} y \,{\mathrm e}^{-2 x}&=4 \left (x^{3}+x^{2}\right ) {\mathrm e}^{-3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.112 |
|
| \begin{align*}
y^{\prime \prime } x +\left (x^{2}+1\right ) y^{\prime }+2 y x&=2 x \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✗ |
✓ |
✓ |
✗ |
36.316 |
|
| \begin{align*}
\left (2+x \right ) y^{\prime \prime }-\left (5+2 x \right ) y^{\prime }+2 y&={\mathrm e}^{x} \left (x +1\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
5.655 |
|
| \begin{align*}
-y+y^{\prime } x +\left (-x^{2}+1\right ) y^{\prime \prime }&=x \left (-x^{2}+1\right )^{{3}/{2}} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
37.660 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-\left (x^{2}+2 x \right ) y^{\prime }+\left (2+x \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
24.298 |
|
| \begin{align*}
t x^{\prime }+y&=0 \\
y^{\prime } t +x&=0 \\
\end{align*} |
system_of_ODEs |
✗ |
✓ |
✓ |
✓ |
0.033 |
|
| \begin{align*}
-y^{\prime } x +y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.903 |
|
| \begin{align*}
\cot \left (y\right )-\tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.851 |
|
| \begin{align*}
x^{3}+x y^{2}+a^{2} y+\left (y^{3}+x^{2} y-a^{2} x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
4.247 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.049 |
|
| \begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.674 |
|
| \begin{align*}
1+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.990 |
|
| \begin{align*}
y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
93.171 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x -2 y-7}{2 x +3 y-6} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.592 |
|
| \begin{align*}
2 x +y+1+\left (4 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.782 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+\sin \left (x \right ) y&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.673 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.767 |
|
| \begin{align*}
\left (x +2 y^{3}\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.132 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.927 |
|
| \begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x^{3} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
7.458 |
|
| \begin{align*}
a^{2}-2 y x -y^{2}-\left (x +y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.671 |
|
| \begin{align*}
x^{2} y-\left (x^{3}+y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.832 |
|
| \begin{align*}
\left (x y \sin \left (y x \right )+\cos \left (y x \right )\right ) y+\left (x y \sin \left (y x \right )-\cos \left (y x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
5.592 |
|
| \begin{align*}
y+\frac {y^{3}}{3}+\frac {x^{2}}{2}+\frac {\left (x y^{2}+x \right ) y^{\prime }}{4}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
2.887 |
|
| \begin{align*}
3 x^{2} y^{4}+2 y x +\left (2 x^{3} y^{2}-x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✗ |
✗ |
✗ |
✗ |
8.062 |
|
| \begin{align*}
y^{3}-2 x^{2} y+\left (2 x y^{2}-x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
31.671 |
|
| \begin{align*}
2 y^{\prime \prime }+9 y^{\prime }-18 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.706 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y^{\prime \prime \prime }-9 y^{\prime \prime }-11 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.076 |
|
| \begin{align*}
y^{\prime \prime \prime }-8 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.050 |
|
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|