| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-2 y^{\prime } x +\left (x^{2}+2\right ) y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.108 |
|
| \begin{align*}
\left (x -2\right )^{2} y^{\prime \prime }-\left (x -2\right ) y^{\prime }-3 y&=0 \\
\end{align*} |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.147 |
|
| \begin{align*}
y^{\prime }-\frac {1}{\sqrt {\operatorname {a4} \,x^{4}+\operatorname {a3} \,x^{3}+\operatorname {a2} \,x^{2}+\operatorname {a1} x +\operatorname {a0}}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.043 |
|
| \begin{align*}
y^{\prime }+a y-c \,{\mathrm e}^{b x}&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.983 |
|
| \begin{align*}
y^{\prime }+a y-b \sin \left (c x \right )&=0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.559 |
|
| \begin{align*}
y^{\prime }+2 y x -x \,{\mathrm e}^{-x^{2}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.441 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{2 x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.619 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )-\frac {\sin \left (2 x \right )}{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.164 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )-{\mathrm e}^{-\sin \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.700 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y-\sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.645 |
|
| \begin{align*}
y^{\prime }-\left (a +\cos \left (\ln \left (x \right )\right )+\sin \left (\ln \left (x \right )\right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.319 |
|
| \begin{align*}
y^{\prime }+y f^{\prime }\left (x \right )-f \left (x \right ) f^{\prime }\left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.309 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) y-g \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.289 |
|
| \begin{align*}
y^{\prime }+y^{2}-1&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.164 |
|
| \begin{align*}
y^{\prime }+y^{2}-a x -b&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.175 |
|
| \begin{align*}
y^{\prime }+y^{2}+a \,x^{m}&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
31.501 |
|
| \begin{align*}
y^{\prime }+y^{2}-2 x^{2} y+x^{4}-2 x -1&=0 \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Riccati] | ✓ | ✓ | ✓ | ✓ | 2.243 |
|
| \begin{align*}
y^{\prime }+y^{2}+\left (y x -1\right ) f \left (x \right )&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.198 |
|
| \begin{align*}
y^{\prime }-y^{2}-3 y+4&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y^{\prime }-y^{2}-y x -x +1&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
3.767 |
|
| \begin{align*}
y^{\prime }-\left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
1.996 |
|
| \begin{align*}
y^{\prime }-y^{2}+\left (x^{2}+1\right ) y-2 x&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.832 |
|
| \begin{align*}
y^{\prime }-y^{2}+y \sin \left (x \right )-\cos \left (x \right )&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.312 |
|
| \begin{align*}
y^{\prime }-y^{2}-y \sin \left (2 x \right )-\cos \left (2 x \right )&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.293 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.674 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b \,x^{\nu }&=0 \\
\end{align*} |
[[_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
32.036 |
|
| \begin{align*}
y^{\prime }+a y^{2}-b \,x^{2 \nu }-c \,x^{\nu -1}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.374 |
|
| \begin{align*}
y^{\prime }-\left (A y-a \right ) \left (B y-b \right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.311 |
|
| \begin{align*}
y^{\prime }+a y \left (y-x \right )-1&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
2.735 |
|
| \begin{align*}
y^{\prime }+x y^{2}-x^{3} y-2 x&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✓ |
4.074 |
|
| \begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.506 |
|
| \begin{align*}
y^{\prime }+x^{-a -1} y^{2}-x^{a}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
50.410 |
|
| \begin{align*}
y^{\prime }-a \,x^{n} \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.663 |
|
| \begin{align*}
y^{\prime }+\sin \left (x \right ) y^{2}-\frac {2 \sin \left (x \right )}{\cos \left (x \right )^{2}}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.554 |
|
| \begin{align*}
y^{\prime }-\frac {y^{2} f^{\prime }\left (x \right )}{g \left (x \right )}+\frac {g^{\prime }\left (x \right )}{f \left (x \right )}&=0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✓ |
✗ |
4.053 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\
\end{align*} | [_Bernoulli] | ✓ | ✓ | ✓ | ✓ | 1.731 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) \left (y^{2}+2 a y+b \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.823 |
|
| \begin{align*}
y^{\prime }+y^{3}+a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
3.081 |
|
| \begin{align*}
y^{\prime }-y^{3}-a \,{\mathrm e}^{x} y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
3.389 |
|
| \begin{align*}
-a y^{3}-\frac {b}{x^{{3}/{2}}}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Abel] |
✓ |
✓ |
✓ |
✗ |
8.134 |
|
| \begin{align*}
y^{\prime }-\operatorname {a3} y^{3}-\operatorname {a2} y^{2}-\operatorname {a1} y-\operatorname {a0}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.129 |
|
| \begin{align*}
y^{\prime }+3 a y^{3}+6 a x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
3.128 |
|
| \begin{align*}
a y^{3} x +b y^{2}+y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✓ |
3.662 |
|
| \begin{align*}
y^{\prime }-x \left (2+x \right ) y^{3}-\left (x +3\right ) y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
3.673 |
|
| \begin{align*}
y^{\prime }+\left (4 a^{2} x +3 a \,x^{2}+b \right ) y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
12.014 |
|
| \begin{align*}
y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.556 |
|
| \begin{align*}
y^{\prime }+2 \left (a^{2} x^{3}-b^{2} x \right ) y^{3}+3 b y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
8.194 |
|
| \begin{align*}
y^{\prime }-x^{a} y^{3}+3 y^{2}-x^{-a} y-x^{-2 a}+a \,x^{-a -1}&=0 \\
\end{align*} |
[_Abel] |
✓ |
✓ |
✓ |
✗ |
4.196 |
|
| \begin{align*}
y^{\prime }-a \left (x^{n}-x \right ) y^{3}-y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
31.342 |
|
| \begin{align*}
y^{\prime }-\left (a \,x^{n}+b x \right ) y^{3}-c y^{2}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
32.436 |
|
| \begin{align*}
y^{\prime }-f_{3} \left (x \right ) y^{3}-f_{2} \left (x \right ) y^{2}-f_{1} \left (x \right ) y-f_{0} \left (x \right )&=0 \\
\end{align*} |
[_Abel] |
✗ |
✗ |
✗ |
✗ |
4.306 |
|
| \begin{align*}
y^{\prime }-\left (y-f \left (x \right )\right ) \left (y-g \left (x \right )\right ) \left (y-\frac {a f \left (x \right )+b g \left (x \right )}{a +b}\right ) h \left (x \right )-\frac {f^{\prime }\left (x \right ) \left (y-g \left (x \right )\right )}{f \left (x \right )-g \left (x \right )}-\frac {g^{\prime }\left (x \right ) \left (y-f \left (x \right )\right )}{g \left (x \right )-f \left (x \right )}&=0 \\
\end{align*} |
[_Abel] |
✗ |
✓ |
✓ |
✗ |
11.550 |
|
| \begin{align*}
y^{\prime }-a y^{n}-b \,x^{\frac {n}{1-n}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
4.525 |
|
| \begin{align*}
y^{\prime }-f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n} \left (a g \left (x \right )+b \right )^{-n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\
\end{align*} |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.823 |
|
| \begin{align*}
y^{\prime }-a^{n} f \left (x \right )^{1-n} g^{\prime }\left (x \right ) y^{n}-\frac {f^{\prime }\left (x \right ) y}{f \left (x \right )}-g^{\prime }\left (x \right ) f \left (x \right )&=0 \\
\end{align*} |
[_Chini, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.281 |
|
| \begin{align*}
y^{\prime }-f \left (x \right ) y^{n}-g \left (x \right ) y-h \left (x \right )&=0 \\
\end{align*} | [_Chini] | ✗ | ✗ | ✗ | ✗ | 1.462 |
|
| \begin{align*}
y^{\prime }-f \left (x \right ) y^{a}-g \left (x \right ) y^{b}&=0 \\
\end{align*} |
[NONE] |
✗ |
✗ |
✗ |
✗ |
1.111 |
|
| \begin{align*}
y^{\prime }-\sqrt {{| y|}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.705 |
|
| \begin{align*}
y^{\prime }-a \sqrt {y}-b x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Chini] |
✓ |
✓ |
✓ |
✗ |
8.155 |
|
| \begin{align*}
y^{\prime }-a \sqrt {1+y^{2}}-b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
46.625 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {y^{2}-1}}{\sqrt {x^{2}-1}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.304 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {x^{2}-1}}{\sqrt {y^{2}-1}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.540 |
|
| \begin{align*}
y^{\prime }-\frac {-x^{2} \sqrt {x^{2}-y^{2}}+y}{x y \sqrt {x^{2}-y^{2}}+x}&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
34.438 |
|
| \begin{align*}
y^{\prime }-\frac {1+y^{2}}{{| y+\sqrt {1+y}|} \left (x +1\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
49.078 |
|
| \begin{align*}
y^{\prime }-\sqrt {\frac {a y^{2}+b y+c}{a \,x^{2}+b x +c}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.060 |
|
| \begin{align*}
y^{\prime }-\sqrt {\frac {y^{3}+1}{x^{3}+1}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
26.889 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {{| y \left (y-1\right ) \left (-1+a y\right )|}}}{\sqrt {{| x \left (x -1\right ) \left (a x -1\right )|}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.106 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {1-y^{4}}}{\sqrt {-x^{4}+1}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.329 |
|
| \begin{align*}
y^{\prime }-\sqrt {\frac {a y^{4}+b y^{2}+1}{a \,x^{4}+b \,x^{2}+1}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
31.802 |
|
| \begin{align*}
y^{\prime }-\sqrt {\left (b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0} \right ) \left (a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0} \right )}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
22.579 |
|
| \begin{align*}
y^{\prime }-\sqrt {\frac {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
20.896 |
|
| \begin{align*}
y^{\prime }-\sqrt {\frac {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}{a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
13.488 |
|
| \begin{align*}
y^{\prime }-\operatorname {R1} \left (x , \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}\right ) \operatorname {R2} \left (y, \sqrt {b_{4} y^{4}+b_{3} y^{3}+b_{2} y^{2}+b_{1} y+b_{0}}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.062 |
|
| \begin{align*}
y^{\prime }-\left (\frac {a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}{a_{0} +a_{1} y+a_{2} y^{2}+a_{3} y^{3}}\right )^{{2}/{3}}&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
10.973 |
|
| \begin{align*}
y^{\prime }-f \left (x \right ) \left (y-g \left (x \right )\right ) \sqrt {\left (y-a \right ) \left (y-b \right )}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
14.566 |
|
| \begin{align*}
y^{\prime }-{\mathrm e}^{x -y}+{\mathrm e}^{x}&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.113 |
|
| \begin{align*}
y^{\prime }-a \cos \left (y\right )+b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
16.967 |
|
| \begin{align*}
y^{\prime }-\cos \left (b x +a y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.338 |
|
| \begin{align*}
y^{\prime }+a \sin \left (\alpha y+\beta x \right )+b&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) \cos \left (a y\right )+g \left (x \right ) \sin \left (a y\right )+h \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
4.828 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) \sin \left (y\right )+\left (1-f^{\prime }\left (x \right )\right ) \cos \left (y\right )-f^{\prime }\left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
2.385 |
|
| \begin{align*}
y^{\prime }+2 \tan \left (y\right ) \tan \left (x \right )-1&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
3.200 |
|
| \begin{align*}
y^{\prime }-a \left (1+\tan \left (y\right )^{2}\right )+\tan \left (y\right ) \tan \left (x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
5.245 |
|
| \begin{align*}
y^{\prime }-\tan \left (y x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✗ |
✗ |
1.168 |
|
| \begin{align*}
y^{\prime }-f \left (a x +b y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.811 |
|
| \begin{align*}
y^{\prime }-x^{a -1} y^{1-b} f \left (\frac {x^{a}}{a}+\frac {y^{b}}{b}\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✗ |
✓ |
✓ |
✗ |
11.251 |
|
| \begin{align*}
y^{\prime }-\frac {y-x f \left (x^{2}+a y^{2}\right )}{x +a y f \left (x^{2}+a y^{2}\right )}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.521 |
|
| \begin{align*}
2 y^{\prime }-3 y^{2}-4 a y-b -c \,{\mathrm e}^{-2 a x}&=0 \\
\end{align*} |
[_Riccati] |
✗ |
✓ |
✓ |
✗ |
33.122 |
|
| \begin{align*}
y^{\prime } x -\sqrt {a^{2}-x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.429 |
|
| \begin{align*}
y^{\prime } x +y-x \sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.757 |
|
| \begin{align*}
y^{\prime } x -y-\frac {x}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.932 |
|
| \begin{align*}
y^{\prime } x -y-x^{2} \sin \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.233 |
|
| \begin{align*}
y^{\prime } x -y-\frac {x \cos \left (\ln \left (\ln \left (x \right )\right )\right )}{\ln \left (x \right )}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.758 |
|
| \begin{align*}
y^{\prime } x +a y+b \,x^{n}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.747 |
|
| \begin{align*}
y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.497 |
|
| \begin{align*}
y^{\prime } x -y^{2}+1&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 2.603 |
|
| \begin{align*}
y^{\prime } x +a y^{2}-y+b \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.427 |
|
| \begin{align*}
y^{\prime } x +a y^{2}-b y+c \,x^{2 b}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.283 |
|
| \begin{align*}
y^{\prime } x +a y^{2}-b y-c \,x^{\beta }&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
31.228 |
|
| \begin{align*}
y^{\prime } x +a +x y^{2}&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
2.796 |
|