| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x \left (3+2 x^{2} y\right ) y^{\prime }+\left (4+3 x^{2} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
243.663 |
|
| \begin{align*}
8 x^{3} y y^{\prime }+3 x^{4}-6 x^{2} y^{2}-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
94.512 |
|
| \begin{align*}
x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.490 |
|
| \begin{align*}
3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.707 |
|
| \begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
49.641 |
|
| \begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.938 |
|
| \begin{align*}
\left (y+1\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.631 |
|
| \begin{align*}
y^{2} y^{\prime }+x \left (2-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.247 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.056 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y&=b x +a \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.191 |
|
| \begin{align*}
\left (x -y^{2}\right ) y^{\prime }&=x^{2}-y \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.665 |
|
| \begin{align*}
y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.639 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
20.928 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
32.967 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }+x \left (x +2 y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.480 |
|
| \begin{align*}
\left (x^{2}+y^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.583 |
|
| \begin{align*}
\left (1-x^{2}+y^{2}\right ) y^{\prime }&=-y^{2}+x^{2}+1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
4.915 |
|
| \begin{align*}
\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+2 y x&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.789 |
|
| \begin{align*}
\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.343 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.198 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
25.152 |
|
| \begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }&=4 x^{3} y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
11.840 |
|
| \begin{align*}
y \left (y+1\right ) y^{\prime }&=x \left (x +1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.334 |
|
| \begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (y+1\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
13.826 |
|
| \begin{align*}
\left (x^{2}+2 y+y^{2}\right ) y^{\prime }+2 x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.357 |
|
| \begin{align*}
\left (x^{3}+2 y-y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
3.753 |
|
| \begin{align*}
\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
7.032 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
27.965 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.620 |
|
| \begin{align*}
\left (x^{2}+2 y x -y^{2}\right ) y^{\prime }+x^{2}-2 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
26.311 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.748 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
59.697 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.484 |
|
| \begin{align*}
\left (a +b +x +y\right )^{2} y^{\prime }&=2 \left (y+a \right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
10.787 |
|
| \begin{align*}
\left (2 x^{2}+4 y x -y^{2}\right ) y^{\prime }&=x^{2}-4 y x -2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.973 |
|
| \begin{align*}
\left (3 x +y\right )^{2} y^{\prime }&=4 \left (3 x +2 y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
50.755 |
|
| \begin{align*}
\left (1-3 x -y\right )^{2} y^{\prime }&=\left (-2 y+1\right ) \left (3-6 x -4 y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
14.933 |
|
| \begin{align*}
\left (\cot \left (x \right )-2 y^{2}\right ) y^{\prime }&=y^{3} \csc \left (x \right ) \sec \left (x \right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✗ |
✓ |
✓ |
✗ |
46.066 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=1+x +a y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.503 |
|
| \begin{align*}
\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.046 |
|
| \begin{align*}
\left (2 x^{2}+3 y^{2}\right ) y^{\prime }+x \left (3 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.954 |
|
| \begin{align*}
3 \left (x^{2}-y^{2}\right ) y^{\prime }+3 \,{\mathrm e}^{x}+6 \left (x +1\right ) x y-2 y^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
5.540 |
|
| \begin{align*}
\left (3 x^{2}+2 y x +4 y^{2}\right ) y^{\prime }+2 x^{2}+6 y x +y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.901 |
|
| \begin{align*}
\left (1-3 x +2 y\right )^{2} y^{\prime }&=\left (4+2 x -3 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
16.602 |
|
| \begin{align*}
\left (1-3 x^{2} y+6 y^{2}\right ) y^{\prime }+x^{2}-3 x y^{2}&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.282 |
|
| \begin{align*}
\left (x -6 y\right )^{2} y^{\prime }+a +2 y x -6 y^{2}&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘]] |
✓ |
✓ |
✓ |
✓ |
4.177 |
|
| \begin{align*}
\left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
22.651 |
|
| \begin{align*}
\left (x^{2}+y x +a y^{2}\right ) y^{\prime }&=a \,x^{2}+y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
108.831 |
|
| \begin{align*}
\left (a \,x^{2}+2 y x -a y^{2}\right ) y^{\prime }+x^{2}-2 a x y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
89.385 |
|
| \begin{align*}
\left (a \,x^{2}+2 b x y+c y^{2}\right ) y^{\prime }+k \,x^{2}+2 a x y+b y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
145.987 |
|
| \begin{align*}
x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.415 |
|
| \begin{align*}
x \left (3 x -y^{2}\right ) y^{\prime }+\left (5 x -2 y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
18.645 |
|
| \begin{align*}
x \left (x^{2}+y^{2}\right ) y^{\prime }&=\left (x^{2}+x^{4}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.562 |
|
| \begin{align*}
x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (-y^{2}+x^{2}+1\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
13.083 |
|
| \begin{align*}
x \left (a -x^{2}-y^{2}\right ) y^{\prime }+\left (a +x^{2}+y^{2}\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
21.872 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
28.632 |
|
| \begin{align*}
\left (x \left (a -x^{2}-y^{2}\right )+y\right ) y^{\prime }+x -\left (a -x^{2}-y^{2}\right ) y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✗ |
12.956 |
|
| \begin{align*}
x \left (y+a \right )^{2} y^{\prime }&=b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.602 |
|
| \begin{align*}
x \left (x^{2}-y x +y^{2}\right ) y^{\prime }+\left (x^{2}+y x +y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
67.832 |
|
| \begin{align*}
x \left (x^{2}-y x -y^{2}\right ) y^{\prime }&=\left (x^{2}+y x -y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
33.581 |
|
| \begin{align*}
x \left (x^{2}+a x y+y^{2}\right ) y^{\prime }&=\left (x^{2}+b x y+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
21.852 |
|
| \begin{align*}
x \left (x^{2}-2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
36.772 |
|
| \begin{align*}
x \left (x^{2}+2 y^{2}\right ) y^{\prime }&=\left (2 x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
37.041 |
|
| \begin{align*}
2 x \left (5 x^{2}+y^{2}\right ) y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
34.059 |
|
| \begin{align*}
x \left (x^{2}+a x y+2 y^{2}\right ) y^{\prime }&=\left (a x +2 y\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
25.797 |
|
| \begin{align*}
3 x y^{2} y^{\prime }&=2 x -y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.994 |
|
| \begin{align*}
\left (1-4 x +3 x y^{2}\right ) y^{\prime }&=\left (2-y^{2}\right ) y \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
5.044 |
|
| \begin{align*}
x \left (x -3 y^{2}\right ) y^{\prime }+\left (2 x -y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
11.555 |
|
| \begin{align*}
3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.642 |
|
| \begin{align*}
x \left (x^{3}-3 x^{3} y+4 y^{2}\right ) y^{\prime }&=6 y^{3} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
5.813 |
|
| \begin{align*}
6 x y^{2} y^{\prime }+x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.723 |
|
| \begin{align*}
x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.771 |
|
| \begin{align*}
x \left (x^{2}-6 y^{2}\right ) y^{\prime }&=4 \left (x^{2}+3 y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
42.397 |
|
| \begin{align*}
x \left (3 x -7 y^{2}\right ) y^{\prime }+\left (5 x -3 y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.355 |
|
| \begin{align*}
x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.012 |
|
| \begin{align*}
\left (1-x^{2} y^{2}\right ) y^{\prime }&=x y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
13.039 |
|
| \begin{align*}
\left (1-x^{2} y^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
1.545 |
|
| \begin{align*}
x \left (1+x y^{2}\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.285 |
|
| \begin{align*}
x \left (1+x y^{2}\right ) y^{\prime }&=\left (2-3 x y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
50.504 |
|
| \begin{align*}
x^{2} \left (y+a \right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.252 |
|
| \begin{align*}
\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.275 |
|
| \begin{align*}
\left (x^{2}+1\right ) \left (1+y^{2}\right ) y^{\prime }+2 x y \left (1-y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.086 |
|
| \begin{align*}
\left (1-x^{3}+6 x^{2} y^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.954 |
|
| \begin{align*}
x \left (3+5 x -12 x y^{2}+4 x^{2} y\right ) y^{\prime }+\left (3+10 x -8 x y^{2}+6 x^{2} y\right ) y&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
5.895 |
|
| \begin{align*}
x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.274 |
|
| \begin{align*}
x \left (-y x +1\right )^{2} y^{\prime }+\left (1+x^{2} y^{2}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
8.730 |
|
| \begin{align*}
\left (1-y^{2} x^{4}\right ) y^{\prime }&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
15.575 |
|
| \begin{align*}
\left (3 x -y^{3}\right ) y^{\prime }&=x^{2}-3 y \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.065 |
|
| \begin{align*}
\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.977 |
|
| \begin{align*}
\left (x^{3}+y^{3}\right ) y^{\prime }+x^{2} \left (a x +3 y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.839 |
|
| \begin{align*}
\left (x -x^{2} y-y^{3}\right ) y^{\prime }&=x^{3}-y+x y^{2} \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.795 |
|
| \begin{align*}
\left (a^{2} x +y \left (x^{2}-y^{2}\right )\right ) y^{\prime }+x \left (x^{2}-y^{2}\right )&=a^{2} y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
5.805 |
|
| \begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
4.573 |
|
| \begin{align*}
\left (3 x^{2}+y^{2}\right ) y y^{\prime }+x \left (x^{2}+3 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.789 |
|
| \begin{align*}
\left (a -3 x^{2}-y^{2}\right ) y y^{\prime }+x \left (a -x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
96.299 |
|
| \begin{align*}
2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.888 |
|
| \begin{align*}
y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.084 |
|
| \begin{align*}
\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
47.866 |
|
| \begin{align*}
\left (5 x^{2}+2 y^{2}\right ) y y^{\prime }+x \left (x^{2}+5 y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.105 |
|
| \begin{align*}
\left (x^{2}-x^{3}+3 x y^{2}+2 y^{3}\right ) y^{\prime }+2 x^{3}+3 x^{2} y+y^{2}-y^{3}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
9.586 |
|