| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.595 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y-a \,x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.166 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-\left (2 x^{2}+1\right ) y-x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.428 |
|
| \begin{align*}
x y^{\prime }+a x y^{2}+2 y+b x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.447 |
|
| \begin{align*}
x y^{\prime }+a x y^{2}+b y+c x +d&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
30.356 |
|
| \begin{align*}
x y^{\prime }+x^{a} y^{2}+\frac {\left (a -b \right ) y}{2}+x^{b}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.381 |
|
| \begin{align*}
x y^{\prime }+a \,x^{\alpha } y^{2}+b y-c \,x^{\beta }&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
1.299 |
|
| \begin{align*}
x y^{\prime }-y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.471 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.630 |
|
| \begin{align*}
x y^{\prime }+f \left (x \right ) \left (y^{2}-x^{2}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.102 |
|
| \begin{align*}
x y^{\prime }+y^{3}+3 x y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
8.128 |
|
| \begin{align*}
x y^{\prime }-y-\sqrt {x^{2}+y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.350 |
|
| \begin{align*}
x y^{\prime }+a \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.751 |
|
| \begin{align*}
x y^{\prime }-x \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
2.349 |
|
| \begin{align*}
x y^{\prime }-x \left (-x +y\right ) \sqrt {x^{2}+y^{2}}-y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
9.529 |
|
| \begin{align*}
x y^{\prime }-{\mathrm e}^{\frac {y}{x}} x -y-x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
7.305 |
|
| \begin{align*}
x y^{\prime }-\ln \left (y\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.042 |
|
| \begin{align*}
x y^{\prime }-y \left (\ln \left (y x \right )-1\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
4.207 |
|
| \begin{align*}
x y^{\prime }-y \left (x \ln \left (\frac {x^{2}}{y}\right )+2\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.837 |
|
| \begin{align*}
x y^{\prime }-\sin \left (x -y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✗ |
✗ |
✗ |
51.100 |
|
| \begin{align*}
x y^{\prime }+\left (\sin \left (y\right )-3 \cos \left (y\right ) x^{2}\right ) \cos \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.016 |
|
| \begin{align*}
x y^{\prime }-y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.607 |
|
| \begin{align*}
x y^{\prime }+x -y+x \cos \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.966 |
|
| \begin{align*}
x y^{\prime }+x \tan \left (\frac {y}{x}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
10.833 |
|
| \begin{align*}
x y^{\prime }-y f \left (y x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
2.160 |
|
| \begin{align*}
x y^{\prime }-y f \left (x^{a} y^{b}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
3.398 |
|
| \begin{align*}
x y^{\prime }+a y-f \left (x \right ) g \left (x^{a} y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
5.757 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.869 |
|
| \begin{align*}
2 x y^{\prime }-y-2 x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.679 |
|
| \begin{align*}
\left (2 x +1\right ) y^{\prime }-4 \,{\mathrm e}^{-y}+2&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
3 x y^{\prime }-3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.652 |
|
| \begin{align*}
x^{2} y^{\prime }+y-x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.601 |
|
| \begin{align*}
x^{2} y^{\prime }-y+x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.246 |
|
| \begin{align*}
x^{2} y^{\prime }-\left (x -1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.441 |
|
| \begin{align*}
x^{2} y^{\prime }+x^{2}+y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.857 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.656 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.197 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+a \,x^{k}-b \left (b -1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.467 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+4 y x +2&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.134 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+y^{2}\right )+a x y+b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.416 |
|
| \begin{align*}
x^{2} \left (y^{\prime }-y^{2}\right )-a \,x^{2} y+a x +2&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.583 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )-b&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
4.205 |
|
| \begin{align*}
x^{2} \left (y^{\prime }+a y^{2}\right )+b \,x^{\alpha }+c&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
72.026 |
|
| \begin{align*}
x^{2} y^{\prime }+a y^{3}-a \,x^{2} y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
2.976 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{3}+a y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
9.863 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{3} a \,x^{2}+b y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
3.938 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -1&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.759 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x -x \left (x^{2}+1\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.357 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x -2 x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.791 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+\left (1+y^{2}\right ) \left (2 y x -1\right )&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
54.425 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )-x \left (x^{2}+1\right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
28.882 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y x +a&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.528 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 y x -\cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.233 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y^{2}-2 y x +1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.174 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.287 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a \left (y^{2}-2 y x +1\right )&=0 \\
\end{align*} |
[_rational, _Riccati] |
✗ |
✓ |
✓ |
✗ |
3.056 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.523 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-2 x y \ln \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.537 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime }+\left (x +2\right ) y^{2}-4 y&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.359 |
|
| \begin{align*}
\left (x^{2}-5 x +6\right ) y^{\prime }+3 y x -8 y+x^{2}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.303 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }+k \left (x +y-a \right ) \left (x +y-b \right )+y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.246 |
|
| \begin{align*}
2 x^{2} y^{\prime }-2 y^{2}-y x +2 a^{2} x&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
2.300 |
|
| \begin{align*}
2 x^{2} y^{\prime }-2 y^{2}-3 y x +2 a^{2} x&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
4.555 |
|
| \begin{align*}
x \left (2 x -1\right ) y^{\prime }+y^{2}-\left (1+4 x \right ) y+4 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.742 |
|
| \begin{align*}
2 x \left (x -1\right ) y^{\prime }+y^{2} \left (x -1\right )-x&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
7.243 |
|
| \begin{align*}
3 x^{2} y^{\prime }-7 y^{2}-3 y x -x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
5.877 |
|
| \begin{align*}
3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-y x -3&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
156.880 |
|
| \begin{align*}
\left (a x +b \right )^{2} y^{\prime }+\left (a x +b \right ) y^{3}+c y^{2}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
17.177 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.681 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.707 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2} x^{4}+x^{2} y+20&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.240 |
|
| \begin{align*}
x^{3} y^{\prime }-x^{6} y^{2}-\left (2 x -3\right ) x^{2} y+3&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.361 |
|
| \begin{align*}
x \left (x^{2}+1\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.256 |
|
| \begin{align*}
x \left (x^{2}-1\right ) y^{\prime }-\left (2 x^{2}-1\right ) y+a \,x^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.294 |
|
| \begin{align*}
x \left (x^{2}-1\right ) y^{\prime }+\left (x^{2}-1\right ) y^{2}-x^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
163.671 |
|
| \begin{align*}
x^{2} \left (x -1\right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.381 |
|
| \begin{align*}
2 x \left (x^{2}-1\right ) y^{\prime }+2 \left (x^{2}-1\right ) y^{2}-\left (3 x^{2}-5\right ) y+x^{2}-3&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| \begin{align*}
3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
76.540 |
|
| \begin{align*}
\left (a \,x^{2}+b x +c \right ) \left (x y^{\prime }-y\right )-y^{2}+x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.138 |
|
| \begin{align*}
x^{4} \left (y^{\prime }+y^{2}\right )+a&=0 \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
5.105 |
|
| \begin{align*}
x \left (x^{3}-1\right ) y^{\prime }-2 x y^{2}+y+x^{2}&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
3.310 |
|
| \begin{align*}
\left (2 x^{4}-x \right ) y^{\prime }-2 \left (x^{3}-1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.330 |
|
| \begin{align*}
\left (a \,x^{2}+b x +c \right )^{2} \left (y^{\prime }+y^{2}\right )+A&=0 \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.952 |
|
| \begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
25.794 |
|
| \begin{align*}
x^{n} y^{\prime }+y^{2}-\left (n -1\right ) x^{n -1} y+x^{2 n -2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.481 |
|
| \begin{align*}
x^{n} y^{\prime }-a y^{2}-b \,x^{2 n -2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.977 |
|
| \begin{align*}
x^{1+2 n} y^{\prime }-a y^{3}-b \,x^{3 n}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Abel] |
✓ |
✓ |
✓ |
✗ |
10.158 |
|
| \begin{align*}
x^{m \left (n -1\right )+n} y^{\prime }-a y^{n}-b \,x^{n \left (m +1\right )}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
6.694 |
|
| \begin{align*}
\sqrt {x^{2}-1}\, y^{\prime }-\sqrt {y^{2}-1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.553 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}-y \sqrt {y^{2}-1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.487 |
|
| \begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+y-\sqrt {a^{2}+x^{2}}+x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.217 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }+y-a x \left (1+\ln \left (x \right )\right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.147 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y^{2} \ln \left (x \right )-\left (2 \ln \left (x \right )^{2}+1\right ) y-\ln \left (x \right )^{3}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
5.390 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-y^{2} \sin \left (x \right )^{2}+\left (\cos \left (x \right )-3 \sin \left (x \right )\right ) y+4&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
0.797 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }+y+\left (1+\sin \left (x \right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.800 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y^{4}-y \sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.279 |
|
| \begin{align*}
\cos \left (x \right ) \sin \left (x \right ) y^{\prime }-y-\sin \left (x \right )^{3}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
6.269 |
|
| \begin{align*}
y^{\prime } \sin \left (2 x \right )+\sin \left (2 y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.190 |
|
| \begin{align*}
\left (a \sin \left (x \right )^{2}+b \right ) y^{\prime }+a y \sin \left (2 x \right )+A x \left (a \sin \left (x \right )^{2}+c \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
18.373 |
|
| \begin{align*}
2 f \left (x \right ) y^{\prime }+2 f \left (x \right ) y^{2}-f^{\prime }\left (x \right ) y-2 f \left (x \right )^{2}&=0 \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
4.121 |
|