| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }&={\mathrm e}^{-2 x} \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.123 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime }&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.179 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
[[_high_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.569 |
|
| \begin{align*}
y^{\prime \prime }+4 y&=x \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
65.669 |
|
| \begin{align*}
y^{\prime \prime }+y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
y^{\prime \prime }-y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
8.448 |
|
| \begin{align*}
y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.169 |
|
| \begin{align*}
y^{\left (5\right )}+y^{\prime \prime \prime \prime }&=x^{2} \\
\end{align*} |
[[_high_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
2 y^{\prime \prime }+3 y^{\prime }-2 y&={\mathrm e}^{x} x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
82.556 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.310 |
|
| \begin{align*}
y^{\prime \prime \prime }-y^{\prime }&=x \sin \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.143 |
|
| \begin{align*}
y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \cos \left (2 x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.190 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }+2 y&=\cos \left (x \right ) x^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
74.823 |
|
| \begin{align*}
y^{\prime \prime }-4 y^{\prime }+3 y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
79.708 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (2 x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
10.341 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{3} \sin \left (2 x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
6.931 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }&={\mathrm e}^{2 x} \sin \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.375 |
|
| \begin{align*}
y^{\prime \prime }-4 y&={\mathrm e}^{2 x} \cos \left (x \right ) x \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
64.579 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }&=x^{2} {\mathrm e}^{-x} \sin \left (x \right ) \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
5.594 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-4 y^{\prime } x +y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
3.898 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+y^{\prime } x +16 y&=0 \\
\end{align*} |
[[_Emden, _Fowler], [_2nd_order, _linear, ‘_with_symmetry_[0,F(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
2.782 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }-16 y^{\prime } x +25 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
1.892 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 y^{\prime } x +10 y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
8.515 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x -18 y&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
6.541 |
|
| \begin{align*}
2 x^{2} y^{\prime \prime }-3 y^{\prime } x +2 y&=\ln \left (x^{2}\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
7.134 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-3 y^{\prime } x +4 y&=x^{3} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.196 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+3 y^{\prime } x +y&=1-x \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
3.799 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }+2 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\frac {1}{x} \\
\end{align*} |
[[_3rd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y&=4 x +\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
5.990 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x +2 y&=x^{2} \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
30.329 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+4 y^{\prime } x +3 y&=\left (x -1\right ) \ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
227.507 |
|
| \begin{align*}
4 x^{3} y^{\prime \prime \prime }+8 x^{2} y^{\prime \prime }-y^{\prime } x +y&=\ln \left (x \right )+x \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.378 |
|
| \begin{align*}
3 x^{3} y^{\prime \prime \prime }+4 x^{2} y^{\prime \prime }-10 y^{\prime } x +10 y&=\frac {4}{x^{2}} \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.441 |
|
| \begin{align*}
x^{4} y^{\prime \prime \prime \prime }+7 x^{3} y^{\prime \prime \prime }+9 x^{2} y^{\prime \prime }-6 y^{\prime } x -6 y&=\cos \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_high_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.675 |
|
| \begin{align*}
x^{3} y^{\prime \prime \prime }-2 x^{2} y^{\prime \prime }-y^{\prime } x +4 y&=\sin \left (\ln \left (x \right )\right ) \\
\end{align*} |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.754 |
|
| \begin{align*}
x^{\prime }-x&=\cos \left (t \right ) \\
y+y^{\prime }&=4 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.544 |
|
| \begin{align*}
x^{\prime }+5 x&=3 t^{2} \\
y+y^{\prime }&={\mathrm e}^{3 t} \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.543 |
|
| \begin{align*}
x^{\prime }+2 x&=3 t \\
x^{\prime }+2 y^{\prime }+y&=\cos \left (2 t \right ) \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.820 |
|
| \begin{align*}
x^{\prime }-x+y&=2 \sin \left (t \right ) \\
x^{\prime }+y^{\prime }&=3 y-3 x \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.691 |
|
| \begin{align*}
2 x^{\prime }+3 x-y&={\mathrm e}^{t} \\
5 x-3 y^{\prime }&=y+2 t \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
1.016 |
|
| \begin{align*}
5 y^{\prime }-3 x^{\prime }-5 y&=5 t \\
3 x^{\prime }-5 y^{\prime }-2 x&=0 \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✗ |
0.280 |
|
| \begin{align*}
x^{\prime }&=3 x \\
y^{\prime }&=2 x+3 y \\
z^{\prime }&=3 y-2 z \\
\end{align*} |
system_of_ODEs |
✓ |
✓ |
✓ |
✓ |
0.608 |
|
| \begin{align*}
y^{\prime \prime }&=\cos \left (t \right ) \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| \begin{align*}
y^{\prime \prime }&=k^{2} y \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.237 |
|
| \begin{align*}
x^{\prime \prime }+k^{2} x&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.329 |
|
| \begin{align*}
y^{3} y^{\prime \prime }+4&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
2.639 |
|
| \begin{align*}
x^{\prime \prime }&=\frac {k^{2}}{x^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
154.849 |
|
| \begin{align*}
y^{\prime \prime } x&=x^{2}+1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.372 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime \prime }&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
1.635 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+2 x \left (1+y^{\prime }\right )&=0 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.421 |
|
| \begin{align*}
y^{\prime \prime }&=y^{\prime }+{y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
8.946 |
|
| \begin{align*}
y^{\prime \prime } x +x&=y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.516 |
|
| \begin{align*}
x^{\prime \prime }+t x^{\prime }&=t^{3} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
7.099 |
|
| \begin{align*}
x^{2} y^{\prime \prime }&=y^{\prime } x +1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.701 |
|
| \begin{align*}
y^{\prime \prime }&=1+{y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
25.815 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime \prime }+y^{\prime } x&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
4.898 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
45.094 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2}+y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
3.506 |
|
| \begin{align*}
y^{\prime \prime }&=y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.349 |
|
| \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]] |
✓ |
✓ |
✓ |
✓ |
8.574 |
|
| \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]] |
✓ |
✓ |
✓ |
✗ |
1.244 |
|
| \begin{align*}
y^{\prime \prime }+2 {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✓ |
1.207 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.783 |
|
| \begin{align*}
y y^{\prime \prime }+1&={y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
4.047 |
|
| \begin{align*}
y^{\prime \prime }&=y \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
2.353 |
|
| \begin{align*}
y y^{\prime \prime }+{y^{\prime }}^{2}&=y y^{\prime } \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.795 |
|
| \begin{align*}
2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.963 |
|
| \begin{align*}
y^{\prime \prime }+2 {y^{\prime }}^{2}&=2 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
7.599 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }&={y^{\prime }}^{3} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
11.433 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime \prime }&=3 {y^{\prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.222 |
|
| \begin{align*}
y^{\prime \prime }&=\sec \left (x \right ) \tan \left (x \right ) \\
y \left (0\right ) &= \frac {\pi }{4} \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
3.335 |
|
| \begin{align*}
2 y^{\prime \prime }&={\mathrm e}^{y} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
1.737 |
|
| \begin{align*}
y^{\prime \prime }&=y^{3} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
0.409 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \cos \left (x \right ) \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✗ |
✗ |
1.105 |
|
| \begin{align*}
y y^{\prime \prime }-y^{2} y^{\prime }&={y^{\prime }}^{2} \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _with_potential_symmetries], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
1.332 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime \prime }+1+{y^{\prime }}^{2}&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✓ |
✓ |
✓ |
7.359 |
|
| \begin{align*}
y y^{\prime \prime }&=y^{3}+{y^{\prime }}^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✗ |
✗ |
5.570 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right )^{2}&=y^{2} y^{\prime \prime } \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= \sqrt {2} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✗ |
✗ |
312.580 |
|
| \begin{align*}
y^{\prime \prime }&={y^{\prime }}^{2} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]] |
✓ |
✗ |
✓ |
✗ |
1.076 |
|
| \begin{align*}
2 y y^{\prime \prime }&=y^{3}+2 {y^{\prime }}^{2} \\
y \left (0\right ) &= -1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✗ |
1.930 |
|
| \begin{align*}
x^{\prime \prime }-k^{2} x&=0 \\
x \left (0\right ) &= 0 \\
x^{\prime }\left (0\right ) &= v_{0} \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
3.429 |
|
| \begin{align*}
y y^{\prime \prime }&=2 {y^{\prime }}^{2}+y^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= \sqrt {3} \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
51.638 |
|
| \begin{align*}
\left (1-{\mathrm e}^{x}\right ) y^{\prime \prime }&={\mathrm e}^{x} y^{\prime } \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
2.267 |
|
| \begin{align*}
4 y^{2}&=x^{2} {y^{\prime }}^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.168 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (x +y\right ) y^{\prime }+1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.714 |
|
| \begin{align*}
1+\left (2 y-x^{2}\right ) {y^{\prime }}^{2}-2 x^{2} y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
11.931 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| \begin{align*}
\left (1-y^{2}\right ) {y^{\prime }}^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.728 |
|
| \begin{align*}
x y {y^{\prime }}^{2}+\left (y x -1\right ) y^{\prime }&=y \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
27.927 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}+y y^{\prime } x -2 x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.814 |
|
| \begin{align*}
y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +2 y^{2}&=x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.866 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +y-2 y x \right ) {y^{\prime }}^{2}-2 y^{\prime } x y \left (x +y\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.286 |
|
| \begin{align*}
y {y^{\prime }}^{2}+\left (y^{2}-x^{3}-x y^{2}\right ) y^{\prime }-x y \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.047 |
|
| \begin{align*}
y&=y^{\prime } x \left (1+y^{\prime }\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.563 |
|
| \begin{align*}
y&=x +3 \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.161 |
|
| \begin{align*}
y \left (1+{y^{\prime }}^{2}\right )&=2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.109 |
|
| \begin{align*}
y {y^{\prime }}^{2}-2 y^{\prime } x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.725 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.061 |
|
| \begin{align*}
x \left (-1+{y^{\prime }}^{2}\right )&=2 y y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.990 |
|
| \begin{align*}
4 x -2 y y^{\prime }+x {y^{\prime }}^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.030 |
|