| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{2} y^{\prime \prime }-\left (3 x^{4}+5 x \right ) y^{\prime }+\left (6 x^{3}+5\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.886 |
|
| \begin{align*}
6 x^{2} y^{\prime \prime }+\left (x^{3}+11 x \right ) y^{\prime }+\left (-2 x^{2}+1\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.862 |
|
| \begin{align*}
x^{2} \left (x +1\right ) y^{\prime \prime }-3 x y^{\prime }+\left (3-2 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.889 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=x^{3}-x +3 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✗ |
0.470 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (-4 x^{3}+x \right ) y^{\prime }-x^{2} y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.727 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-5 x y^{\prime }+\left (-x^{2}+9\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-x \right ) y^{\prime }+y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.667 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+5 x y^{\prime }+\left (2 x +4\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.743 |
|
| \begin{align*}
x y^{\prime \prime }+\left (1-x \right ) y^{\prime }+2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[_Laguerre] |
✓ |
✓ |
✓ |
✓ |
0.776 |
|
| \begin{align*}
x y^{\prime \prime }+2 y^{\prime }-3 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
2.529 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+2 x^{4} y^{\prime }-2 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.474 |
|
| \begin{align*}
4 x^{2} y^{\prime \prime }+8 x y^{\prime }+\left (2 x -3\right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.242 |
|
| \begin{align*}
9 x^{2} y^{\prime \prime }+\left (x^{2}-15 x \right ) y^{\prime }+7 y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.846 |
|
| \begin{align*}
x^{2} y^{\prime \prime }+\left (x^{2}-5 x \right ) y^{\prime }+\left (5-6 x \right ) y&=0 \\
\end{align*}
Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.338 |
|
| \begin{align*}
y^{\prime }&=2 y \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.432 |
|
| \begin{align*}
y^{\prime }&=x +2 y \\
y \left (0\right ) &= 2 \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.427 |
|
| \begin{align*}
y^{\prime }-y&=x^{2}+1 \\
y \left (0\right ) &= 1 \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.404 |
|
| \begin{align*}
y^{\prime }-y&=x^{2}+1 \\
y \left (0\right ) &= -3 \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{\prime }-7 y&=-x^{4}+2 \\
y \left (0\right ) &= a \\
\end{align*}
Series expansion around \(x=0\). |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.483 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.901 |
|
| \begin{align*}
\sin \left (x \right ) \sin \left (y\right )+\cos \left (x \right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.697 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.000 |
|
| \begin{align*}
2 y-3 x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.426 |
|
| \begin{align*}
m y-n x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.055 |
|
| \begin{align*}
y^{\prime }&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.175 |
|
| \begin{align*}
v^{\prime }&=-\frac {v}{p} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.933 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x}-\left (4+{\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.441 |
|
| \begin{align*}
1&=b \left (\cos \left (y\right )+x \sin \left (y\right ) y^{\prime }\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.968 |
|
| \begin{align*}
y x -\left (x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.654 |
|
| \begin{align*}
x^{2}+y \left (x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.151 |
|
| \begin{align*}
y x +x -\left (1+x^{2}+y^{2}+x^{2} y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.969 |
|
| \begin{align*}
x \cos \left (y\right )^{2}+\tan \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.673 |
|
| \begin{align*}
x y^{3}+\left (y+1\right ) {\mathrm e}^{-x} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.005 |
|
| \begin{align*}
\theta ^{\prime }&=z \left (-z^{2}+1\right ) \sec \left (\theta \right )^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.937 |
|
| \begin{align*}
x^{\prime }&=\sin \left (x\right )^{2} \cos \left (t \right )^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.404 |
|
| \begin{align*}
x y^{\prime }+y+x y \left (y^{\prime }+1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.203 |
|
| \begin{align*}
\cos \left (y\right )&=x y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.202 |
|
| \begin{align*}
1+\ln \left (x \right )+\left (1+\ln \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.986 |
|
| \begin{align*}
x -\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.642 |
|
| \begin{align*}
x +\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
a^{2}-x y^{\prime } \sqrt {-a^{2}+x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.067 |
|
| \begin{align*}
y-\left ({\mathrm e}^{3 x}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.401 |
|
| \begin{align*}
y \ln \left (x \right ) \ln \left (y\right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.664 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.803 |
|
| \begin{align*}
r^{\prime }&=-2 r t \\
r \left (0\right ) &= r_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.265 |
|
| \begin{align*}
x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\
y \left (\infty \right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.170 |
|
| \begin{align*}
\left (2 a^{2}-r^{2}\right ) r^{\prime }&=r^{3} \sin \left (\theta \right ) \\
r \left (0\right ) &= a \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
4.625 |
|
| \begin{align*}
y^{\prime }&=x \,{\mathrm e}^{-y-x^{2}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.497 |
|
| \begin{align*}
v v^{\prime }&=g \\
v \left (x_{0} \right ) &= v_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
1.972 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.502 |
|
| \begin{align*}
y x -\left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.698 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.231 |
|
| \begin{align*}
2 x^{2}+y x -2 y^{2}-\left (x^{2}-4 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.911 |
|
| \begin{align*}
x^{2}+2 y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.590 |
|
| \begin{align*}
\left (x -y\right ) \left (4 x +y\right )+x \left (5 x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
97.486 |
|
| \begin{align*}
5 v-u +\left (3 v-7 u \right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
60.165 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
15.602 |
|
| \begin{align*}
x^{2}+2 y x -4 y^{2}-\left (x^{2}-8 y x -4 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
13.846 |
|
| \begin{align*}
x \left (x^{2}+y^{2}\right )^{2} \left (-x y^{\prime }+y\right )+y^{6} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.188 |
|
| \begin{align*}
x y y^{\prime }+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.015 |
|
| \begin{align*}
y x -\left (x +2 y\right )^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.774 |
|
| \begin{align*}
v^{2}+x \left (x +v\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
72.504 |
|
| \begin{align*}
x \csc \left (\frac {y}{x}\right )-y+x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.421 |
|
| \begin{align*}
x +\sin \left (\frac {y}{x}\right )^{2} \left (-x y^{\prime }+y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
19.274 |
|
| \begin{align*}
x -\ln \left (y\right ) y+y \ln \left (x \right )+x \left (\ln \left (y\right )-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
13.803 |
|
| \begin{align*}
x -y \arctan \left (\frac {y}{x}\right )+x \arctan \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
24.667 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \left (x y^{\prime }-y\right ) {\mathrm e}^{\frac {x}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.258 |
|
| \begin{align*}
t \left (s^{2}+t^{2}\right ) s^{\prime }-s \left (s^{2}-t^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
16.031 |
|
| \begin{align*}
y-\left (x +\sqrt {y^{2}-x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.861 |
|
| \begin{align*}
x -y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (2\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.809 |
|
| \begin{align*}
y-\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
13.115 |
|
| \begin{align*}
y+\sqrt {x^{2}+y^{2}}-x y^{\prime }&=0 \\
y \left (\sqrt {3}\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.291 |
|
| \begin{align*}
x \cos \left (\frac {y}{x}\right )^{2}-y+x y^{\prime }&=0 \\
y \left (1\right ) &= \frac {\pi }{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.523 |
|
| \begin{align*}
y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.977 |
|
| \begin{align*}
y^{2}+\left (x^{2}+3 y x +4 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.284 |
|
| \begin{align*}
y x +2 \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
42.006 |
|
| \begin{align*}
y \left (2 x^{2}-y x +y^{2}\right )-x^{2} \left (2 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
35.355 |
|
| \begin{align*}
y \left (9 x -2 y\right )-x \left (6 x -y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
101.601 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x \left (3 x^{2}-5 y^{2}\right ) y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
39.986 |
|
| \begin{align*}
16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \\
y \left (1\right ) &= -3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
74.984 |
|
| \begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.652 |
|
| \begin{align*}
-2 y x +\left (3 x^{2}-2 y^{2}\right ) y^{\prime }&=0 \\
y \left (0\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
86.477 |
|
| \begin{align*}
x +y+\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
23.576 |
|
| \begin{align*}
6 x +y^{2}+y \left (2 x -3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.845 |
|
| \begin{align*}
2 y x -3 x^{2}+\left (x^{2}+y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
4.434 |
|
| \begin{align*}
y^{2}-2 y x +6 x -\left (x^{2}-2 y x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.628 |
|
| \begin{align*}
2 y x -y+\left (x^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.689 |
|
| \begin{align*}
v \left (2 u v^{2}-3\right )+\left (3 u^{2} v^{2}-3 u +4 v\right ) v^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.327 |
|
| \begin{align*}
\cos \left (2 y\right )-3 x^{2} y^{2}+\left (\cos \left (2 y\right )-2 x \sin \left (2 y\right )-2 x^{3} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.885 |
|
| \begin{align*}
1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.145 |
|
| \begin{align*}
1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.515 |
|
| \begin{align*}
w^{3}+w z^{2}-z+\left (z^{3}+w^{2} z-w \right ) z^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.303 |
|
| \begin{align*}
2 y x -\tan \left (y\right )+\left (x^{2}-x \sec \left (y\right )^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.867 |
|
| \begin{align*}
\cos \left (x \right ) \cos \left (y\right )-\cot \left (x \right )-\sin \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✓ |
28.871 |
|
| \begin{align*}
x +\sin \left (y\right )-\cos \left (y\right )-x \cos \left (y\right ) \left (2 \sin \left (y\right ) x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
183.086 |
|
| \begin{align*}
\left (6+3 y x -4 y^{3}\right ) x +\left (x^{3}-6 x^{2} y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.355 |
|
| \begin{align*}
\sin \left (y\right )-2 x \cos \left (y\right )^{2}+x \cos \left (y\right ) \left (2 \sin \left (y\right ) x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
4.329 |
|
| \begin{align*}
2 x +y \cos \left (y x \right )+x \cos \left (y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.017 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
12.621 |
|
| \begin{align*}
\left (y^{2}-x^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.927 |
|