| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
x^{5} y^{\prime }&=1-3 x^{4} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.270 |
|
| \begin{align*}
x \left (-x^{4}+1\right ) y^{\prime }&=2 x \left (x^{2}-y^{2}\right )+\left (-x^{4}+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.266 |
|
| \begin{align*}
x^{7} y^{\prime }+5 x^{3} y^{2}+2 \left (x^{2}+1\right ) y^{3}&=0 \\
\end{align*} |
[_rational, _Abel] |
✗ |
✓ |
✓ |
✗ |
58.840 |
|
| \begin{align*}
x^{n} y^{\prime }&=a +b \,x^{n -1} y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
5.034 |
|
| \begin{align*}
x^{n} y^{\prime }&=x^{2 n -1}-y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
179.474 |
|
| \begin{align*}
x^{n} y^{\prime }+x^{2 n -2}+y^{2}+\left (1-n \right ) x^{n -1} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
6.694 |
|
| \begin{align*}
x^{n} y^{\prime }&=a^{2} x^{2 n -2}+b^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _Riccati] |
✓ |
✓ |
✓ |
✗ |
8.734 |
|
| \begin{align*}
x^{n} y^{\prime }&=x^{n -1} \left (a \,x^{2 n}+n y-b y^{2}\right ) \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
5.793 |
|
| \begin{align*}
x^{k} y^{\prime }&=a \,x^{m}+b y^{n} \\
\end{align*} |
[_Chini] |
✗ |
✗ |
✗ |
✗ |
5.048 |
|
| \begin{align*}
\sqrt {x^{2}+1}\, y^{\prime }&=2 x -y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.543 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.171 |
|
| \begin{align*}
\left (x -\sqrt {x^{2}+1}\right ) y^{\prime }&=y+\sqrt {1+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.335 |
|
| \begin{align*}
y^{\prime } \sqrt {a^{2}+x^{2}}+x +y&=\sqrt {a^{2}+x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.999 |
|
| \begin{align*}
y^{\prime } \sqrt {b^{2}+x^{2}}&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.904 |
|
| \begin{align*}
y^{\prime } \sqrt {b^{2}-x^{2}}&=\sqrt {a^{2}-y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.841 |
|
| \begin{align*}
x y^{\prime } \sqrt {a^{2}+x^{2}}&=y \sqrt {b^{2}+y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.992 |
|
| \begin{align*}
x y^{\prime } \sqrt {-a^{2}+x^{2}}&=y \sqrt {y^{2}-b^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.281 |
|
| \begin{align*}
x^{{3}/{2}} y^{\prime }&=a +b \,x^{{3}/{2}} y^{2} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.245 |
|
| \begin{align*}
y^{\prime } \sqrt {x^{3}+1}&=\sqrt {y^{3}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.653 |
|
| \begin{align*}
y^{\prime } \sqrt {x \left (1-x \right ) \left (-a x +1\right )}&=\sqrt {y \left (1-y\right ) \left (1-a y\right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.320 |
|
| \begin{align*}
y^{\prime } \sqrt {-x^{4}+1}&=\sqrt {1-y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \begin{align*}
y^{\prime } \sqrt {x^{4}+x^{2}+1}&=\sqrt {1+y^{2}+y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.160 |
|
| \begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
y^{\prime } \sqrt {b \,x^{4}+a \,x^{2}+1}+\sqrt {1+a y^{2}+b y^{4}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.340 |
|
| \begin{align*}
y^{\prime } \sqrt {a_{4} x^{4}+a_{3} x^{3}+a_{2} x^{2}+a_{1} x +a_{0}}&=\sqrt {b_{0} +b_{1} y+b_{2} y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.749 |
|
| \begin{align*}
y^{\prime } \left (x^{3}+1\right )^{{2}/{3}}+\left (y^{3}+1\right )^{{2}/{3}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.450 |
|
| \begin{align*}
y^{\prime } \left (4 x^{3}+a_{1} x +a_{0} \right )^{{2}/{3}}+\left (a_{0} +a_{1} y+4 y^{3}\right )^{{2}/{3}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.381 |
|
| \begin{align*}
y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )&=y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
10.105 |
|
| \begin{align*}
\left (1-4 \cos \left (x \right )^{2}\right ) y^{\prime }&=\tan \left (x \right ) \left (1+4 \cos \left (x \right )^{2}\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.586 |
|
| \begin{align*}
\left (1-\sin \left (x \right )\right ) y^{\prime }+\cos \left (x \right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.903 |
|
| \begin{align*}
\left (\cos \left (x \right )-\sin \left (x \right )\right ) y^{\prime }+\left (\cos \left (x \right )+\sin \left (x \right )\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.298 |
|
| \begin{align*}
\left (a_{0} +a_{1} \sin \left (x \right )^{2}\right ) y^{\prime }+a_{2} x \left (a_{3} +a_{1} \sin \left (x \right )^{2}\right )+a_{1} y \sin \left (2 x \right )&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
13.531 |
|
| \begin{align*}
\left (x -{\mathrm e}^{x}\right ) y^{\prime }+x \,{\mathrm e}^{x}+\left (1-{\mathrm e}^{x}\right ) y&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.681 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }&=a x \left (1+\ln \left (x \right )\right )-y \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.812 |
|
| \begin{align*}
y y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.984 |
|
| \begin{align*}
y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.461 |
|
| \begin{align*}
y y^{\prime }+x^{3}+y&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
7.607 |
|
| \begin{align*}
y y^{\prime }+a x +b y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
108.688 |
|
| \begin{align*}
y y^{\prime }+x \,{\mathrm e}^{-x} \left (1+y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.086 |
|
| \begin{align*}
y y^{\prime }+f \left (x \right )&=g \left (x \right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
✗ |
✗ |
✗ |
6.835 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| \begin{align*}
y y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.113 |
|
| \begin{align*}
y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.727 |
|
| \begin{align*}
y y^{\prime }&=a_{0} +a_{1} y+a_{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.412 |
|
| \begin{align*}
y y^{\prime }&=a x +b x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.696 |
|
| \begin{align*}
y y^{\prime }&=\csc \left (x \right )^{2}-y^{2} \cot \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.302 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {y^{2}+a^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.644 |
|
| \begin{align*}
y y^{\prime }&=\sqrt {y^{2}-a^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.375 |
|
| \begin{align*}
y y^{\prime }+x +f \left (x^{2}+y^{2}\right ) g \left (x \right )&=0 \\
\end{align*} |
[NONE] |
✗ |
✓ |
✓ |
✗ |
5.749 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=x +y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
37.797 |
|
| \begin{align*}
\left (1+y\right ) y^{\prime }&=x^{2} \left (1-y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.112 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.899 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.211 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.549 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }&=x -y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.339 |
|
| \begin{align*}
1-y^{\prime }&=x +y \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.621 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=y \left (2 y x +1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
15.857 |
|
| \begin{align*}
\left (x +y\right ) y^{\prime }+\tan \left (y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.700 |
|
| \begin{align*}
\left (x -y\right ) y^{\prime }&=\left ({\mathrm e}^{-\frac {x}{y}}+1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
11.363 |
|
| \begin{align*}
\left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
25.397 |
|
| \begin{align*}
\left (x +y+2\right ) y^{\prime }&=-x -y+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.565 |
|
| \begin{align*}
\left (3-x -y\right ) y^{\prime }&=1+x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.148 |
|
| \begin{align*}
\left (3-x +y\right ) y^{\prime }&=11-4 x +3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
28.020 |
|
| \begin{align*}
\left (2 x +y\right ) y^{\prime }+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
9.168 |
|
| \begin{align*}
\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.059 |
|
| \begin{align*}
\left (2 x -y+3\right ) y^{\prime }+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.522 |
|
| \begin{align*}
\left (4+2 x -y\right ) y^{\prime }+5+x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.654 |
|
| \begin{align*}
\left (5-2 x -y\right ) y^{\prime }+4-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.837 |
|
| \begin{align*}
\left (1-3 x +y\right ) y^{\prime }&=2 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.804 |
|
| \begin{align*}
\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.724 |
|
| \begin{align*}
\left (4 x -y\right ) y^{\prime }+2 x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.046 |
|
| \begin{align*}
\left (6-4 x -y\right ) y^{\prime }&=2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
10.345 |
|
| \begin{align*}
\left (1+5 x -y\right ) y^{\prime }+5+x -5 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
6.561 |
|
| \begin{align*}
\left (a +b x +y\right ) y^{\prime }+a -b x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.301 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }+x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✓ |
1.362 |
|
| \begin{align*}
\left (x^{2}-y\right ) y^{\prime }&=4 y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.209 |
|
| \begin{align*}
\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+\cos \left (x \right ) y\right ) y&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
67.403 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.677 |
|
| \begin{align*}
2 y y^{\prime }&=x y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.875 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.413 |
|
| \begin{align*}
\left (x +2 y\right ) y^{\prime }+2 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.222 |
|
| \begin{align*}
\left (x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.970 |
|
| \begin{align*}
\left (x -2 y+1\right ) y^{\prime }&=1+2 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.404 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+1-x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.855 |
|
| \begin{align*}
\left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
12.870 |
|
| \begin{align*}
2 \left (x +y\right ) y^{\prime }+x^{2}+2 y&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.484 |
|
| \begin{align*}
\left (3+2 x -2 y\right ) y^{\prime }&=1+6 x -2 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
\left (1-4 x -2 y\right ) y^{\prime }+2 x +y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.964 |
|
| \begin{align*}
\left (6 x -2 y\right ) y^{\prime }&=2+3 x -y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.429 |
|
| \begin{align*}
\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
30.340 |
|
| \begin{align*}
\left (x^{3}+2 y\right ) y^{\prime }&=3 x \left (2-y x \right ) \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.355 |
|
| \begin{align*}
\left (\sec \left (x \right ) \tan \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 \sin \left (x \right ) y\right ) y&=0 \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
67.737 |
|
| \begin{align*}
\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime }&=2 \,{\mathrm e}^{-2 x} x -\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \\
\end{align*} |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
5.992 |
|
| \begin{align*}
3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.041 |
|
| \begin{align*}
3 \left (2-y\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.757 |
|
| \begin{align*}
\left (x -3 y\right ) y^{\prime }+4+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
74.259 |
|
| \begin{align*}
\left (4-x -3 y\right ) y^{\prime }+3-x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.302 |
|
| \begin{align*}
\left (2 x +3 y+2\right ) y^{\prime }&=1-2 x -3 y \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.278 |
|
| \begin{align*}
\left (-3 y-2 x +5\right ) y^{\prime }+1-2 x -3 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.413 |
|
| \begin{align*}
\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.492 |
|