| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\frac {y \cos \left (\frac {y}{x}\right )}{x}-\left (\frac {x \sin \left (\frac {y}{x}\right )}{y}+\cos \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
49.798 |
|
| \begin{align*}
y+x \ln \left (\frac {y}{x}\right ) y^{\prime }-2 x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
123.645 |
|
| \begin{align*}
2 \,{\mathrm e}^{\frac {x}{y}} y+\left (y-2 x \,{\mathrm e}^{\frac {x}{y}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
40.250 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x -\sin \left (\frac {y}{x}\right ) y+x \sin \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
39.883 |
|
| \begin{align*}
x^{2}+y^{2}&=2 x y y^{\prime } \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
74.717 |
|
| \begin{align*}
{\mathrm e}^{\frac {y}{x}} x +y&=x y^{\prime } \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
59.353 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}+\csc \left (\frac {y}{x}\right )&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
23.149 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.686 |
|
| \begin{align*}
x +2 y-4-\left (2 x -4 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
59.892 |
|
| \begin{align*}
3 x +2 y+1-\left (3 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.400 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.352 |
|
| \begin{align*}
x +y-1+\left (2 x +2 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
36.086 |
|
| \begin{align*}
x +y-1-\left (x -y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
68.105 |
|
| \begin{align*}
x +y+\left (2 x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
32.970 |
|
| \begin{align*}
7 y-3+\left (2 x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.941 |
|
| \begin{align*}
x +2 y+\left (3 x +6 y+3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
35.659 |
|
| \begin{align*}
x +2 y+\left (-1+y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.704 |
|
| \begin{align*}
3 x -2 y+4-\left (2 x +7 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
75.375 |
|
| \begin{align*}
x +y+\left (3 x +3 y-4\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✗ |
✗ |
38.230 |
|
| \begin{align*}
3 x +2 y+3-\left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
107.801 |
|
| \begin{align*}
y+7+\left (2 x +y+3\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
30.803 |
|
| \begin{align*}
x +y+2-\left (x -y-4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
68.154 |
|
| \begin{align*}
3 x^{2} y+8 x y^{2}+\left (x^{3}+8 x^{2} y+12 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.856 |
|
| \begin{align*}
\frac {1+2 y x}{y}+\frac {\left (-x +y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.441 |
|
| \begin{align*}
2 y x +\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.331 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.823 |
|
| \begin{align*}
\cos \left (y\right )-\left (\sin \left (y\right ) x -y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.895 |
|
| \begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
7.066 |
|
| \begin{align*}
x^{2}-x +y^{2}-\left ({\mathrm e}^{y}-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
8.446 |
|
| \begin{align*}
2 x +\cos \left (x \right ) y+\left (2 y+\sin \left (x \right )-\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.707 |
|
| \begin{align*}
x \sqrt {x^{2}+y^{2}}-\frac {x^{2} y y^{\prime }}{y-\sqrt {x^{2}+y^{2}}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.941 |
|
| \begin{align*}
4 x^{3}-\sin \left (x \right )+y^{3}-\left (y^{2}+1-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.626 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{3}+x y^{3}+1\right )+3 y^{2} \left (x \,{\mathrm e}^{x}-6\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.772 |
|
| \begin{align*}
\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (\frac {\pi }{4}\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.428 |
|
| \begin{align*}
y^{2} {\mathrm e}^{x y^{2}}+4 x^{3}+\left (2 x y \,{\mathrm e}^{x y^{2}}-3 y^{2}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.912 |
|
| \begin{align*}
y^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.426 |
|
| \begin{align*}
y \sec \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.687 |
|
| \begin{align*}
{\mathrm e}^{x}-\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
0.681 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.369 |
|
| \begin{align*}
y^{3}+x y^{2}+y+\left (x^{3}+x^{2} y+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
✓ |
✗ |
3.990 |
|
| \begin{align*}
3 y-x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y-3 x y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.405 |
|
| \begin{align*}
y \left (2 x^{2} y^{3}+3\right )+x \left (x^{2} y^{3}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
38.673 |
|
| \begin{align*}
2 y x +x^{2}+\left (x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.411 |
|
| \begin{align*}
x^{2}+\cos \left (x \right ) y+\left (y^{3}+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.740 |
|
| \begin{align*}
x^{2}+y^{2}+x +x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.448 |
|
| \begin{align*}
x -2 y x +{\mathrm e}^{y}+\left (y-x^{2}+x \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.925 |
|
| \begin{align*}
{\mathrm e}^{x} \sin \left (y\right )+{\mathrm e}^{-y}-\left (x \,{\mathrm e}^{-y}-{\mathrm e}^{x} \cos \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| \begin{align*}
x^{2}-y^{2}-y-\left (x^{2}-y^{2}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational] |
✓ |
✓ |
✓ |
✓ |
13.109 |
|
| \begin{align*}
y^{2} x^{4}-y+\left (x^{2} y^{4}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
0.840 |
|
| \begin{align*}
y \left (2 x +y^{3}\right )-x \left (2 x -y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
0.572 |
|
| \begin{align*}
\arctan \left (y x \right )+\frac {y x -2 x y^{2}}{1+x^{2} y^{2}}+\frac {\left (x^{2}-2 x^{2} y\right ) y^{\prime }}{1+x^{2} y^{2}}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
2.316 |
|
| \begin{align*}
{\mathrm e}^{x} \left (x +1\right )+\left (-x \,{\mathrm e}^{x}+y \,{\mathrm e}^{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
1.143 |
|
| \begin{align*}
\frac {y x +1}{y}+\frac {\left (-x +2 y\right ) y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
2.559 |
|
| \begin{align*}
y^{2}-3 y x -2 x^{2}+\left (y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.369 |
|
| \begin{align*}
\left (2 x +y+1\right ) y-x \left (x +2 y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.313 |
|
| \begin{align*}
y \left (2 x -y-1\right )+x \left (2 y-x -1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✗ |
1.393 |
|
| \begin{align*}
y^{2}+12 x^{2} y+\left (2 y x +4 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
x \left (2 x +3 y\right ) y^{\prime }+3 \left (x +y\right )^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.233 |
|
| \begin{align*}
y-\left (x^{2}+y^{2}+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
7.566 |
|
| \begin{align*}
2 y x +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.708 |
|
| \begin{align*}
2 y x +x^{2}+b +\left (a +x^{2}+y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.714 |
|
| \begin{align*}
x y^{\prime }+y&=x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
13.448 |
|
| \begin{align*}
y^{\prime }+a y&=b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.954 |
|
| \begin{align*}
x y^{\prime }+y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.763 |
|
| \begin{align*}
x^{\prime }+2 x y&={\mathrm e}^{-y^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.754 |
|
| \begin{align*}
r^{\prime }&=\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.796 |
|
| \begin{align*}
y^{\prime }-\frac {2 x y}{x^{2}+1}&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.516 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.138 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.888 |
|
| \begin{align*}
\tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.174 |
|
| \begin{align*}
2 y+y^{\prime }&=3 \,{\mathrm e}^{-2 x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.422 |
|
| \begin{align*}
2 y+y^{\prime }&=\frac {3 \,{\mathrm e}^{-2 x}}{4} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.063 |
|
| \begin{align*}
2 y+y^{\prime }&=\sin \left (x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.774 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&={\mathrm e}^{2 x} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.326 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.638 |
|
| \begin{align*}
x y^{\prime }+y&=x \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.415 |
|
| \begin{align*}
x y^{\prime }-y&=x^{2} \sin \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.387 |
|
| \begin{align*}
x y^{\prime }+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.484 |
|
| \begin{align*}
x y^{\prime }-y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.345 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
21.606 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.576 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
112.611 |
|
| \begin{align*}
2 \cos \left (x \right ) y^{\prime }&=y \sin \left (x \right )-y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.734 |
|
| \begin{align*}
\left (x -\cos \left (y\right )\right ) y^{\prime }+\tan \left (y\right )&=0 \\
y \left (1\right ) &= \frac {\pi }{6} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
37.994 |
|
| \begin{align*}
y^{\prime }&=x^{3}+\frac {2 y}{x}-\frac {y^{2}}{x} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
7.971 |
|
| \begin{align*}
y^{\prime }&=2 \sec \left (x \right ) \tan \left (x \right )-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_Riccati] |
✓ |
✓ |
✓ |
✗ |
1.844 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{x^{2}}-\frac {y}{x}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
32.737 |
|
| \begin{align*}
y^{\prime }&=1+\frac {y}{x}-\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
46.384 |
|
| \begin{align*}
2 x y y^{\prime }+\left (x +1\right ) y^{2}&={\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.315 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
7.075 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y-1&=\left (x +1\right ) \sqrt {y+1} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
34.682 |
|
| \begin{align*}
{\mathrm e}^{y} \left (y^{\prime }+1\right )&={\mathrm e}^{x} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.392 |
|
| \begin{align*}
y^{\prime } \sin \left (y\right )+\sin \left (x \right ) \cos \left (y\right )&=\sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.723 |
|
| \begin{align*}
\left (x -y\right )^{2} y^{\prime }&=4 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
21.859 |
|
| \begin{align*}
x y^{\prime }-y&=\sqrt {x^{2}+y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
60.513 |
|
| \begin{align*}
\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
63.796 |
|
| \begin{align*}
\left (x^{2}-y^{2}\right ) y^{\prime }&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
62.535 |
|
| \begin{align*}
y+\left (1+y^{2} {\mathrm e}^{2 x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
11.151 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.592 |
|