| # |
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‘]] |
✓ |
✓ |
✓ |
✗ |
12.228 |
|
| \begin{align*}
8 x^{3} y y^{\prime }+3 x^{4}-6 y^{2} x^{2}-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.892 |
|
| \begin{align*}
x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.936 |
|
| \begin{align*}
3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.483 |
|
| \begin{align*}
x^{7} y y^{\prime }&=2 x^{2}+2+5 x^{3} y \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✗ |
✓ |
✓ |
✗ |
26.961 |
|
| \begin{align*}
y y^{\prime } \sqrt {x^{2}+1}+x \sqrt {1+y^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.882 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime } \sqrt {x^{2}+1}&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.273 |
|
| \begin{align*}
y^{2} y^{\prime }+x \left (2-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.576 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.553 |
|
| \begin{align*}
\left (x +y^{2}\right ) y^{\prime }+y&=b x +a \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.862 |
|
| \begin{align*}
\left (x -y^{2}\right ) y^{\prime }&=x^{2}-y \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.509 |
|
| \begin{align*}
y x +\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.067 |
|
| \begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.276 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.364 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
0.980 |
|
| \begin{align*}
\left (y^{2}+x^{2}\right ) y^{\prime }+2 x \left (2 x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.668 |
|
| \begin{align*}
\left (1-x^{2}+y^{2}\right ) y^{\prime }&=1+x^{2}-y^{2} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _rational] | ✓ | ✓ | ✓ | ✓ | 1.765 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
1.607 |
|
| \begin{align*}
\left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+b^{2}+x^{2}+2 y x&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.964 |
|
| \begin{align*}
\left (x^{2}+y^{2}+x \right ) y^{\prime }&=y \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
1.446 |
|
| \begin{align*}
\left (3 x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.451 |
|
| \begin{align*}
\left (x^{4}+y^{2}\right ) y^{\prime }&=4 x^{3} y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.927 |
|
| \begin{align*}
y \left (1+y\right ) y^{\prime }&=x \left (x +1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
1.810 |
|
| \begin{align*}
\left (x +2 y+y^{2}\right ) y^{\prime }+y \left (1+y\right )+\left (x +y\right )^{2} y^{2}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
4.971 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
1.356 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✗ |
1.611 |
|
| \begin{align*}
\left (1+y+y x +y^{2}\right ) y^{\prime }+1+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
2.425 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.908 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.841 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
6.714 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=\left (-x -y+1\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.477 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=\left (x +y+2\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
51.966 |
|
| \begin{align*}
\left (x +y\right )^{2} y^{\prime }&=x^{2}-2 y x +5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.687 |
|
| \begin{align*}
\left (a +b +x +y\right )^{2} y^{\prime }&=2 \left (a +y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
4.849 |
|
| \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] | ✓ | ✓ | ✓ | ✗ | 0.932 |
|
| \begin{align*}
\left (3 x +y\right )^{2} y^{\prime }&=4 \left (2 y+3 x \right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
35.259 |
|
| \begin{align*}
\left (1-3 x -y\right )^{2} y^{\prime }&=\left (1-2 y\right ) \left (3-6 x -4 y\right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational] |
✓ |
✓ |
✓ |
✗ |
5.516 |
|
| \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*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
51.961 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=1+x +a y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.994 |
|
| \begin{align*}
\left (x^{2}-3 y^{2}\right ) y^{\prime }+1+2 y x&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.648 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
6.166 |
|
| \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’)‘] |
✓ |
✓ |
✓ |
✗ |
2.671 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
1.048 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
8.264 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.085 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✓ |
1.924 |
|
| \begin{align*}
\left (x^{2}+a y^{2}\right ) y^{\prime }&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.857 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
109.470 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
20.525 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
125.619 |
|
| \begin{align*}
x \left (1-y^{2}\right ) y^{\prime }&=\left (x^{2}+1\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.740 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
7.963 |
|
| \begin{align*}
x \left (y^{2}+x^{2}\right ) y^{\prime }&=\left (x^{2}+x^{4}+y^{2}\right ) y \\
\end{align*} | [[_homogeneous, ‘class D‘], _rational] | ✓ | ✓ | ✓ | ✗ | 2.226 |
|
| \begin{align*}
x \left (1-x^{2}+y^{2}\right ) y^{\prime }+\left (1+x^{2}-y^{2}\right ) y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✓ |
✓ |
✓ |
✗ |
3.717 |
|
| \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)]‘]] |
✓ |
✓ |
✓ |
✗ |
4.102 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
10.568 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.125 |
|
| \begin{align*}
x \left (a +y\right )^{2} y^{\prime }&=b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.510 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
65.270 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
13.029 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
12.478 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
13.078 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
14.290 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
16.223 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
18.040 |
|
| \begin{align*}
3 y^{2} y^{\prime } x&=2 x -y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.827 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✗ |
2.246 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.316 |
|
| \begin{align*}
3 x \left (x +y^{2}\right ) y^{\prime }+x^{3}-3 y x -2 y^{3}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.144 |
|
| \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]‘]] |
✓ |
✓ |
✓ |
✓ |
2.326 |
|
| \begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} | [[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] | ✓ | ✓ | ✓ | ✓ | 3.059 |
|
| \begin{align*}
x \left (x +6 y^{2}\right ) y^{\prime }+y x -3 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
4.356 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
18.486 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
4.330 |
|
| \begin{align*}
x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.131 |
|
| \begin{align*}
\left (1-y^{2} x^{2}\right ) y^{\prime }&=x y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.681 |
|
| \begin{align*}
\left (1-y^{2} x^{2}\right ) y^{\prime }&=\left (y x +1\right ) y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.535 |
|
| \begin{align*}
x \left (x y^{2}+1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
2.692 |
|
| \begin{align*}
x \left (x y^{2}+1\right ) y^{\prime }&=\left (2-3 x y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
14.599 |
|
| \begin{align*}
x^{2} \left (a +y\right )^{2} y^{\prime }&=\left (x^{2}+1\right ) \left (y^{2}+a^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.348 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
3.891 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| \begin{align*}
\left (1-x^{3}+6 y^{2} x^{2}\right ) y^{\prime }&=\left (6+3 y x -4 y^{3}\right ) x \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.379 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.950 |
|
| \begin{align*}
x^{3} \left (1+y^{2}\right ) y^{\prime }+3 x^{2} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.730 |
|
| \begin{align*}
x \left (-y x +1\right )^{2} y^{\prime }+\left (y^{2} x^{2}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.493 |
|
| \begin{align*}
\left (1-x^{4} y^{2}\right ) y^{\prime }&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
7.224 |
|
| \begin{align*}
\left (3 x -y^{3}\right ) y^{\prime }&=x^{2}-3 y \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
1.818 |
|
| \begin{align*}
\left (x^{3}-y^{3}\right ) y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.529 |
|
| \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] | ✓ | ✓ | ✓ | ✗ | 1.128 |
|
| \begin{align*}
\left (x -x^{2} y-y^{3}\right ) y^{\prime }&=x^{3}-y+x y^{2} \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.316 |
|
| \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] |
✓ |
✗ |
✓ |
✗ |
2.766 |
|
| \begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }&=x \left (a -x^{2}-y^{2}\right ) \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.217 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
14.815 |
|
| \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] |
✗ |
✓ |
✓ |
✗ |
4.422 |
|
| \begin{align*}
2 y^{3} y^{\prime }&=x^{3}-x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.336 |
|
| \begin{align*}
y \left (2 y^{2}+1\right ) y^{\prime }&=x \left (2 x^{2}+1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.252 |
|
| \begin{align*}
\left (3 x^{2}+2 y^{2}\right ) y y^{\prime }+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
16.611 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
1.125 |
|
| \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] |
✗ |
✓ |
✓ |
✗ |
4.761 |
|