| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.644 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y&=x^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.246 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.850 |
|
| \begin{align*}
y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2 y&=x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.227 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.724 |
|
| \begin{align*}
y^{\prime \prime }+y&=\tan \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.884 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=x^{2}+\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=2 x \,{\mathrm e}^{2 x}-\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.637 |
|
| \begin{align*}
y^{\prime \prime }+y&=2 \,{\mathrm e}^{x}+x^{3}-x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.761 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{2 x}-\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.260 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=x^{2} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.201 |
|
| \begin{align*}
-3 y^{\prime }-2 y^{\prime \prime }+y^{\prime \prime \prime }&=3 x^{2}+\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.409 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=4+{\mathrm e}^{x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.262 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{2 x}+1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.738 |
|
| \begin{align*}
y+2 y^{\prime \prime }+y^{\prime \prime \prime \prime }&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| \begin{align*}
-y+x y^{\prime }+x^{3} y^{\prime \prime \prime }&=x \ln \left (x \right ) \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.559 |
|
| \begin{align*}
2 y+2 x^{2} y^{\prime \prime }+x^{3} y^{\prime \prime \prime }&=10 x +\frac {10}{x} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.118 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
9.950 |
|
| \begin{align*}
\left (x +1\right )^{2} y^{\prime \prime }-\left (x +1\right ) y^{\prime }+6 y&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.395 |
|
| \begin{align*}
6 y-5 y^{\prime }+y^{\prime \prime }&=\cos \left (x \right )-{\mathrm e}^{2 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.034 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&={\mathrm e}^{x} \cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.219 |
|
| \begin{align*}
y+2 y^{\prime }+y^{\prime \prime }&=2 x^{3}-x \,{\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.945 |
|
| \begin{align*}
-4 y^{\prime }+y^{\prime \prime \prime }&=-3 \,{\mathrm e}^{2 x}+x^{2} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.271 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=\cos \left (x \right ) \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.248 |
|
| \begin{align*}
y+3 x y^{\prime }+9 x^{2} y^{\prime \prime }+6 x^{3} y^{\prime \prime \prime }+x^{4} y^{\prime \prime \prime \prime }&=\left (1+\ln \left (x \right )\right )^{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=x^{2}-x \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.249 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sin \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.074 |
|
| \begin{align*}
4 y+y^{\prime \prime }&=\sec \left (x \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.998 |
|
| \begin{align*}
-2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \\
\end{align*} |
[[_high_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.268 |
|
| \begin{align*}
y^{\prime \prime }+y&=x \cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.055 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-x y^{\prime }+y&=\frac {1}{x} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.556 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=x \,{\mathrm e}^{x}+\cos \left (x \right )^{2} \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.797 |
|
| \begin{align*}
y x -x^{2} y^{\prime }+y^{\prime \prime }&=x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
4.312 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.837 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x y^{\prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.749 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.480 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }+2 \cos \left (x \right ) y^{\prime }+3 y \sin \left (x \right )&={\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
2.164 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.163 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+4 x^{3} y^{\prime }+\left (x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
10.722 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-y x&=2 \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.838 |
|
| \begin{align*}
y^{\prime \prime }+\left (2 \,{\mathrm e}^{x}-1\right ) y^{\prime }+y \,{\mathrm e}^{2 x}&={\mathrm e}^{4 x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
4.300 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }+4 y&=0 \\
\end{align*} |
[_Gegenbauer, [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.091 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
3.669 |
|
| \begin{align*}
y+3 x^{5} y^{\prime }+x^{6} y^{\prime \prime }&=\frac {1}{x^{2}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
3.934 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.797 |
|
| \begin{align*}
3 y-\left (x +3\right ) y^{\prime }+x y^{\prime \prime }&=0 \\
\end{align*} |
[_Laguerre] |
✓ |
✓ |
✓ |
✗ |
1.076 |
|
| \begin{align*}
\left (x -3\right ) y^{\prime \prime }-\left (4 x -9\right ) y^{\prime }+\left (3 x -6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.174 |
|
| \begin{align*}
\left (-x^{2}+2\right ) y+4 x y^{\prime }+x^{2} y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.124 |
|
| \begin{align*}
2 y-2 x y^{\prime }+\left (x^{2}+1\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.654 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
0.619 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 x y^{\prime }+\left (x^{2}+6\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
\left (2 x^{3}-1\right ) y^{\prime \prime }-6 x^{2} y^{\prime }+6 y x&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
1.776 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
2.319 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 n x \left (x +1\right ) y^{\prime }+\left (a^{2} x^{2}+n^{2}+n \right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
12.832 |
|
| \begin{align*}
x^{4} y^{\prime \prime }+2 x^{3} \left (x +1\right ) y^{\prime }+n^{2} y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✗ |
✓ |
✗ |
✗ |
20.143 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
1.036 |
|
| \begin{align*}
\left (x y^{\prime \prime \prime }-y^{\prime \prime }\right )^{2}&={y^{\prime \prime \prime }}^{2}+1 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.864 |
|
| \begin{align*}
y^{\prime \prime }+x y^{\prime }&=x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.616 |
|
| \begin{align*}
y^{\prime \prime }&=x \,{\mathrm e}^{x} \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.546 |
|
| \begin{align*}
\left (y^{\prime }-x y^{\prime \prime }\right )^{2}&=1+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.520 |
|
| \begin{align*}
y y^{\prime \prime }-y^{2} y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.858 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
7.919 |
|
| \begin{align*}
2 y^{\prime \prime }&={\mathrm e}^{y} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
18.336 |
|
| \begin{align*}
y y^{\prime \prime }+2 y^{\prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.616 |
|
| \begin{align*}
-2 y+2 x y^{\prime }-x^{2} y^{\prime \prime }+\left (x^{2}-2 x +2\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.042 |
|
| \begin{align*}
y-x y^{\prime }-y^{\prime \prime }+x y^{\prime \prime \prime }&=-x^{2}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.039 |
|
| \begin{align*}
y^{\prime }+\left (x +2\right ) y^{\prime \prime }+\left (x +2\right )^{2} y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.863 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.504 |
|
| \begin{align*}
\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y&=\cos \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
20.750 |
|
| \begin{align*}
\left (x^{3}-x \right ) y^{\prime \prime \prime }+\left (8 x^{2}-3\right ) y^{\prime \prime }+14 x y^{\prime }+4 y&=0 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.650 |
|
| \begin{align*}
2 x^{3} y y^{\prime \prime \prime }+6 x^{3} y^{\prime } y^{\prime \prime }+18 x^{2} y y^{\prime \prime }+18 {y^{\prime }}^{2} x^{2}+36 x y y^{\prime }+6 y^{2}&=0 \\
\end{align*} |
[[_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.044 |
|
| \begin{align*}
x^{5} y^{\prime \prime }+\left (2 x^{4}-x \right ) y^{\prime }-\left (2 x^{3}-1\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.715 |
|
| \begin{align*}
x^{2} y^{\prime \prime \prime }-5 x y^{\prime \prime }+\left (4 x^{4}+5\right ) y^{\prime }-8 x^{3} y&=0 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.041 |
|
| \begin{align*}
y^{\prime \prime }+2 \cot \left (x \right ) y^{\prime }+2 \tan \left (x \right ) {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✗ |
✓ |
1.780 |
|
| \begin{align*}
\left (x y^{\prime }-y\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]] |
✗ |
✓ |
✓ |
✗ |
0.594 |
|
| \begin{align*}
x^{3} y^{\prime \prime }-\left (x y^{\prime }-y\right )^{2}&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.735 |
|
| \begin{align*}
y y^{\prime \prime }-{y^{\prime }}^{2}&=\ln \left (y\right ) y^{2}-x^{2} y^{2} \\
\end{align*} |
[[_2nd_order, _reducible, _mu_xy]] |
✗ |
✓ |
✓ |
✗ |
0.488 |
|
| \begin{align*}
\sin \left (x \right )^{2} y^{\prime \prime }-2 y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.232 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
6.408 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=2 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.592 |
|
| \begin{align*}
y y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
2.005 |
|
| \begin{align*}
6 y+18 x y^{\prime }+9 x^{2} y^{\prime \prime }+\left (x^{3}+1\right ) y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _fully, _exact, _linear]] |
✓ |
✓ |
✓ |
✗ |
0.474 |
|
| \begin{align*}
\left (x^{2}-x \right ) y^{\prime \prime }+\left (4 x +2\right ) y^{\prime }+2 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.434 |
|
| \begin{align*}
\left (1+\ln \left (y\right )\right ) {y^{\prime }}^{2}+\left (1-\ln \left (y\right )\right ) y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.892 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.103 |
|
| \begin{align*}
x^{2}+2 y+4 \left (x +y\right ) y^{\prime }+2 {y^{\prime }}^{2} x +x \left (x +2 y\right ) y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.732 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
5.557 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }-\frac {y^{\prime }}{x}+x^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
1.914 |
|
| \begin{align*}
y^{\prime }+8 x y^{\prime \prime }+4 x^{2} y^{\prime \prime \prime }&=0 \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.423 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime \prime }-\cos \left (x \right ) y^{\prime }+2 y \sin \left (x \right )&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✗ |
1.570 |
|
| \begin{align*}
3 x^{\prime }+3 x+2 y&={\mathrm e}^{t} \\
4 x-3 y^{\prime }+3 y&=3 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.228 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.268 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.992 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.506 |
|
| \begin{align*}
x^{\prime \prime }+2 x^{\prime }+2 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.505 |
|
| \begin{align*}
x^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.599 |
|
| \begin{align*}
x^{\prime }+2 x&=t^{2}+4 t +7 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| \begin{align*}
2 x^{\prime } t&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.815 |
|
| \begin{align*}
t^{2} x^{\prime \prime }-6 x&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.473 |
|
| \begin{align*}
2 x^{\prime \prime }-5 x^{\prime }-3 x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.433 |
|