| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime \prime \prime }-2 y^{\prime \prime }-5 y^{\prime }+6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x y^{\prime }-12 y&=2 x^{2} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.020 |
|
| \begin{align*}
y+\left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.551 |
|
| \begin{align*}
y^{\prime }&=3 \sin \left (x \right ) \\
y \left (\pi \right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{\prime }&=4 \,{\mathrm e}^{-t}-2 \\
x \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.672 |
|
| \begin{align*}
x^{\prime \prime }&=t^{2}-4 t +8 \\
x \left (0\right ) &= 1 \\
x^{\prime }\left (0\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.806 |
|
| \begin{align*}
s^{\prime }&=9 \sqrt {u} \\
s \left (4\right ) &= 16 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.663 |
|
| \begin{align*}
y^{\prime \prime }&=12 x \left (4-x \right ) \\
y \left (0\right ) &= 7 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.293 |
|
| \begin{align*}
y^{\prime }&=-\frac {4}{x^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.351 |
|
| \begin{align*}
y^{\prime \prime }&=1-\cos \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| \begin{align*}
y^{\prime \prime }&=\sqrt {2 x +1} \\
y \left (0\right ) &= 5 \\
y \left (4\right ) &= -3 \\
\end{align*} |
[[_2nd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| \begin{align*}
y^{\prime }-2 y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.329 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.355 |
|
| \begin{align*}
y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \\
\end{align*} |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.098 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-x y^{\prime }+y&=0 \\
\end{align*} |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.876 |
|
| \begin{align*}
y^{\prime \prime }+3 y^{\prime }-4 y&=0 \\
y \left (0\right ) &= 3 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.485 |
|
| \begin{align*}
y^{\prime \prime }+y^{2}&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✓ |
13.965 |
|
| \begin{align*}
y^{\prime }&=1+2 y x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.973 |
|
| \begin{align*}
y^{\prime }&=\frac {-x +3}{y+5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.756 |
|
| \begin{align*}
y^{\prime \prime \prime }&=-24 \cos \left (\frac {\pi x}{2}\right ) \\
y \left (0\right ) &= -4 \\
y \left (1\right ) &= 0 \\
y^{\prime }\left (1\right ) &= 6 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
x y {y^{\prime }}^{2}-\left (x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
y^{\prime }&=y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.250 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.364 |
|
| \begin{align*}
y^{\prime }&=\sec \left (y\right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.597 |
|
| \begin{align*}
1+{y^{\prime }}^{2}+2 y y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]] |
✓ |
✓ |
✓ |
✗ |
8.174 |
|
| \begin{align*}
y^{\prime }+y \tan \left (x \right )&=0 \\
y \left (\pi \right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.898 |
|
| \begin{align*}
y^{\prime \prime }-y&=4 x \\
y \left (0\right ) &= 2 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.698 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y}{-x +y} \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
39.967 |
|
| \begin{align*}
y^{\prime \prime \prime }&=0 \\
y \left (0\right ) &= 1 \\
y \left (1\right ) &= 2 \\
y \left (2\right ) &= 9 \\
\end{align*} |
[[_3rd_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
2 y y^{\prime }+{y^{\prime }}^{2} x +x y y^{\prime \prime }&=0 \\
y \left (3\right ) &= 1 \\
y^{\prime }\left (3\right ) &= 2 \\
\end{align*} |
[[_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]] |
✓ |
✓ |
✓ |
✗ |
3.346 |
|
| \begin{align*}
y^{\prime \prime }+y&={\mathrm e}^{-x^{2}} \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.117 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.164 |
|
| \begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.644 |
|
| \begin{align*}
y^{\prime \prime }+\lambda y&=0 \\
y \left (0\right ) &= 0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
5.337 |
|
| \begin{align*}
\left (y^{\prime }-2 x \right ) \left (y^{\prime }-3 x^{2}\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.449 |
|
| \begin{align*}
{| y^{\prime }|}+1&=0 \\
\end{align*} |
[_sym_implicit] |
✗ |
✓ |
✗ |
✗ |
0.325 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.677 |
|
| \begin{align*}
{| y^{\prime }|}+{| y|}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
10.814 |
|
| \begin{align*}
y^{\prime }&=3 x +2 y \\
y \left (1\right ) &= 4 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.132 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
4.783 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+y^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
4.256 |
|
| \begin{align*}
y^{\prime }+y x&=x^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.109 |
|
| \begin{align*}
y^{\prime }&=\frac {x -2 y}{y-2 x} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
67.833 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}-y^{2}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
6.122 |
|
| \begin{align*}
y^{\prime }&=x^{2}+y^{2} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_Riccati, _special]] |
✗ |
✓ |
✓ |
✗ |
91.779 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y x} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
103.142 |
|
| \begin{align*}
y^{\prime }&=y \csc \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✗ |
✗ |
✗ |
✗ |
49.074 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{\sqrt {x^{2}+4 y^{2}-4}} \\
y \left (3\right ) &= 2 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
24.682 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.452 |
|
| \begin{align*}
y^{\prime }&=2 x -y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.013 |
|
| \begin{align*}
y^{\prime }&=2 x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.109 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.055 |
|
| \begin{align*}
y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.655 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}+4 y^{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✗ |
✗ |
4.968 |
|
| \begin{align*}
y^{\prime }&=\sqrt {-x +y}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.764 |
|
| \begin{align*}
y^{\prime \prime }+{y^{\prime }}^{2} x&=1 \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
3.411 |
|
| \begin{align*}
x y^{\prime \prime }+y^{\prime }+y x&=0 \\
y \left (1\right ) &= 2 \\
y^{\prime }\left (1\right ) &= 0 \\
\end{align*} |
[_Lienard] |
✓ |
✓ |
✓ |
✓ |
1.860 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (\sqrt {y x +1}-1\right )^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
24.460 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.495 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.937 |
|
| \begin{align*}
3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.542 |
|
| \begin{align*}
2 y+{\mathrm e}^{-3 x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.045 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}+x}{4 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.670 |
|
| \begin{align*}
x y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.016 |
|
| \begin{align*}
\sin \left (y\right )^{2}+\cos \left (x \right )^{2} y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.239 |
|
| \begin{align*}
x \sqrt {1+y^{2}}&=y y^{\prime } \sqrt {x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.897 |
|
| \begin{align*}
2 \cos \left (x \right ) y+3 \sin \left (x \right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.782 |
|
| \begin{align*}
y^{\prime }&=8 y x +3 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.680 |
|
| \begin{align*}
i^{\prime }+5 i&=10 \\
i \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.246 |
|
| \begin{align*}
y+\left (x^{3}+x^{3} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.478 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.667 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (-1+y\right ) \left (y+3\right )}{\left (-2+y\right ) \left (x +3\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.217 |
|
| \begin{align*}
r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\
r \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.088 |
|
| \begin{align*}
r^{\prime }&=\frac {\sin \left (t \right )+{\mathrm e}^{r} \sin \left (t \right )}{3 \,{\mathrm e}^{r}+{\mathrm e}^{r} \cos \left (2 t \right )} \\
r \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.866 |
|
| \begin{align*}
x^{3} {\mathrm e}^{2 x^{2}+3 y^{2}}-y^{3} {\mathrm e}^{-x^{2}-2 y^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.553 |
|
| \begin{align*}
U^{\prime }&=\frac {U+1}{\sqrt {s}+\sqrt {s U}} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
66.487 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.757 |
|
| \begin{align*}
x^{2}+y \sin \left (y x \right )+x \sin \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.621 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.932 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.042 |
|
| \begin{align*}
x y^{\prime }&=2 x +3 y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
12.427 |
|
| \begin{align*}
x^{2}-y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.269 |
|
| \begin{align*}
x +2+\left (2 x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
45.917 |
|
| \begin{align*}
y^{\prime }&=\frac {y+\cos \left (\frac {y}{x}\right )^{2}}{x} \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘]] |
✓ |
✓ |
✓ |
✗ |
8.254 |
|
| \begin{align*}
x y^{\prime }&=y-\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.693 |
|
| \begin{align*}
y&=\left (2 x +3 y\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
82.610 |
|
| \begin{align*}
x^{3}+y^{3}-x y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.598 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.470 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\sec \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.966 |
|
| \begin{align*}
x -4 y+\left (3 x -2\right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
8.720 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {x^{2}+y^{2}}}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
53.872 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +5 y}{2 x -y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
146.321 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-5 y x -2 y^{2}}{6 x^{2}-8 y x +y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
44.560 |
|
| \begin{align*}
y^{\prime }&=\left (x +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.071 |
|
| \begin{align*}
y^{\prime }&=\sqrt {2 x +3 y} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.613 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +3 y+1}{3 x -2 y-5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
34.838 |
|
| \begin{align*}
\left (3 x -y-9\right ) y^{\prime }&=10-2 x +2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
215.521 |
|
| \begin{align*}
2 x +3 y+4&=\left (4 x +6 y+1\right ) y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
19.717 |
|
| \begin{align*}
2 x +2 y+1+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.679 |
|
| \begin{align*}
2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
102.507 |
|