| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\left (a +x^{2}+y^{2}\right ) y y^{\prime }+x \left (y^{2}+x^{2}-a \right )&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.921 |
|
| \begin{align*}
2 y^{3} y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.818 |
|
| \begin{align*}
\left (2 y^{3}+y\right ) y^{\prime }-2 x^{3}-x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.169 |
|
| \begin{align*}
\left (2 y^{3}+5 x^{2} y\right ) y^{\prime }+5 x y^{2}+x^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.695 |
|
| \begin{align*}
\left (3 x^{3}+6 x^{2} y-3 x y^{2}+20 y^{3}\right ) y^{\prime }+4 x^{3}+9 x^{2} y+6 x y^{2}-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
28.096 |
|
| \begin{align*}
\left (\frac {y^{2}}{b}+\frac {x^{2}}{a}\right ) \left (y y^{\prime }+x \right )+\frac {\left (a -b \right ) \left (y y^{\prime }-x \right )}{a +b}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
206.154 |
|
| \begin{align*}
\left (2 a y^{3}+3 a x y^{2}-b \,x^{3}+c \,x^{2}\right ) y^{\prime }-a y^{3}+c y^{2}+3 b \,x^{2} y+2 b \,x^{3}&=0 \\
\end{align*} |
[_rational] |
✗ |
✓ |
✓ |
✗ |
7.639 |
|
| \begin{align*}
x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.181 |
|
| \begin{align*}
\left (2 x y^{3}-x^{4}\right ) y^{\prime }+2 x^{3} y-y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
103.984 |
|
| \begin{align*}
\left (2 x y^{3}+y\right ) y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
0.729 |
|
| \begin{align*}
\left (2 x y^{3}+y x +x^{2}\right ) y^{\prime }-y x +y^{2}&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.560 |
|
| \begin{align*}
\left (3 x y^{3}-4 y x +y\right ) y^{\prime }+y^{2} \left (y^{2}-2\right )&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
1.101 |
|
| \begin{align*}
\left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✗ |
3.486 |
|
| \begin{align*}
\left (x^{2} y^{3}+y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.156 |
|
| \begin{align*}
\left (2 x^{2} y^{3}+x^{2} y^{2}-2 x \right ) y^{\prime }-2 y-1&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.797 |
|
| \begin{align*}
\left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 x y^{4}+x&=0 \\
\end{align*} |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.187 |
|
| \begin{align*}
\left (a x y^{3}+c \right ) x y^{\prime }+\left (b \,x^{3} y+c \right ) y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
3.383 |
|
| \begin{align*}
\left (2 x^{3} y^{3}-x \right ) y^{\prime }+2 x^{3} y^{3}-y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
2.956 |
|
| \begin{align*}
y \left (y^{3}-2 x^{3}\right ) y^{\prime }+\left (2 y^{3}-x^{3}\right ) x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
139.227 |
|
| \begin{align*}
y \left (\left (b x +a y\right )^{3}+b \,x^{3}\right ) y^{\prime }+x \left (\left (b x +a y\right )^{3}+a y^{3}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
44.650 |
|
| \begin{align*}
\left (x +2 y+2 x^{2} y^{3}+x y^{4}\right ) y^{\prime }+y^{5}+y&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✗ |
4.829 |
|
| \begin{align*}
a \,x^{2} y^{n} y^{\prime }-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.194 |
|
| \begin{align*}
y^{m} x^{n} \left (a x y^{\prime }+b y\right )+\alpha x y^{\prime }+\beta y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
15.475 |
|
| \begin{align*}
\left (f \left (x +y\right )+1\right ) y^{\prime }+f \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.509 |
|
| \begin{align*}
\left (\sqrt {y x}-1\right ) x y^{\prime }-\left (\sqrt {y x}+1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
17.472 |
|
| \begin{align*}
\left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✗ |
59.385 |
|
| \begin{align*}
\left (1+\sqrt {x +y}\right ) y^{\prime }+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
2.988 |
|
| \begin{align*}
\sqrt {y^{2}-1}\, y^{\prime }-\sqrt {x^{2}-1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.924 |
|
| \begin{align*}
\left (\sqrt {1+y^{2}}+a x \right ) y^{\prime }+\sqrt {x^{2}+1}+a y&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
27.958 |
|
| \begin{align*}
\left (x +\sqrt {x^{2}+y^{2}}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.564 |
|
| \begin{align*}
\left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
89.131 |
|
| \begin{align*}
\left (x \sqrt {1+x^{2}+y^{2}}-y \left (x^{2}+y^{2}\right )\right ) y^{\prime }-y \sqrt {1+x^{2}+y^{2}}-x \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
7.416 |
|
| \begin{align*}
\left (\frac {\operatorname {e1} \left (x +a \right )}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2} \left (x -a \right )}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right ) y^{\prime }-y \left (\frac {\operatorname {e1}}{\left (\left (x +a \right )^{2}+y^{2}\right )^{{3}/{2}}}+\frac {\operatorname {e2}}{\left (\left (x -a \right )^{2}+y^{2}\right )^{{3}/{2}}}\right )&=0 \\
\end{align*} |
unknown |
✓ |
✗ |
✗ |
✗ |
24.221 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+x \,{\mathrm e}^{y}\right ) y^{\prime }+y \,{\mathrm e}^{x}+{\mathrm e}^{y}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.139 |
|
| \begin{align*}
x \left (3 \,{\mathrm e}^{y x}+2 \,{\mathrm e}^{-y x}\right ) \left (x y^{\prime }+y\right )+1&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
15.047 |
|
| \begin{align*}
\left (\ln \left (y\right )+x \right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.115 |
|
| \begin{align*}
\left (-1+2 x +\ln \left (y\right )\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
x \left (2 x^{2} y \ln \left (y\right )+1\right ) y^{\prime }-2 y&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
3.789 |
|
| \begin{align*}
x \left (y \ln \left (y x \right )+y-a x \right ) y^{\prime }-y \left (a x \ln \left (y x \right )-y+a x \right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
3.964 |
|
| \begin{align*}
y^{\prime } \left (1+\sin \left (x \right )\right ) \sin \left (y\right )+\cos \left (x \right ) \left (\cos \left (y\right )-1\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.976 |
|
| \begin{align*}
\sin \left (y\right )+\cos \left (x \right ) y+\left (x \cos \left (y\right )+\sin \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
13.288 |
|
| \begin{align*}
x y^{\prime } \cot \left (\frac {y}{x}\right )+2 x \sin \left (\frac {y}{x}\right )-y \cot \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
27.825 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }-\cos \left (x \right ) \sin \left (y\right )^{2}-\sin \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
37.694 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }+x \sin \left (y\right ) \cos \left (y\right )^{2}-\sin \left (y\right )^{3}&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
61.663 |
|
| \begin{align*}
y^{\prime } \left (\cos \left (y\right )-\sin \left (\alpha \right ) \sin \left (x \right )\right ) \cos \left (y\right )+\left (\cos \left (x \right )-\sin \left (\alpha \right ) \sin \left (y\right )\right ) \cos \left (x \right )&=0 \\
\end{align*} |
unknown |
✓ |
✓ |
✓ |
✗ |
35.649 |
|
| \begin{align*}
x \cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.260 |
|
| \begin{align*}
\left (\sin \left (y\right ) x -1\right ) y^{\prime }+\cos \left (y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
9.466 |
|
| \begin{align*}
\left (x \cos \left (y\right )+\cos \left (x \right )\right ) y^{\prime }-y \sin \left (x \right )+\sin \left (y\right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
29.329 |
|
| \begin{align*}
\left (\cos \left (y\right ) x^{2}+2 y \sin \left (x \right )\right ) y^{\prime }+2 \sin \left (y\right ) x +y^{2} \cos \left (x \right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
29.421 |
|
| \begin{align*}
x y^{\prime } \ln \left (x \right ) \sin \left (y\right )+\cos \left (y\right ) \left (1-x \cos \left (y\right )\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✓ |
43.100 |
|
| \begin{align*}
\sin \left (x \right ) \cos \left (y\right )+\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.083 |
|
| \begin{align*}
3 \sin \left (x \right ) \sin \left (y\right ) y^{\prime }+5 \cos \left (x \right )^{4} y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.821 |
|
| \begin{align*}
y^{\prime } \cos \left (a y\right )-b \left (1-c \cos \left (a y\right )\right ) \sqrt {\cos \left (a y\right )^{2}-1+c \cos \left (a y\right )}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
31.483 |
|
| \begin{align*}
\left (x \sin \left (y x \right )+\cos \left (x +y\right )-\sin \left (y\right )\right ) y^{\prime }+y \sin \left (y x \right )+\cos \left (x +y\right )+\cos \left (x \right )&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
10.215 |
|
| \begin{align*}
\left (x^{2} y \sin \left (y x \right )-4 x \right ) y^{\prime }+x y^{2} \sin \left (y x \right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
8.800 |
|
| \begin{align*}
\left (x y^{\prime }-y\right ) \cos \left (\frac {y}{x}\right )^{2}+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
20.518 |
|
| \begin{align*}
\left (\sin \left (\frac {y}{x}\right ) y-x \cos \left (\frac {y}{x}\right )\right ) x y^{\prime }-\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.756 |
|
| \begin{align*}
\left (y f \left (x^{2}+y^{2}\right )-x \right ) y^{\prime }+y+x f \left (x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
26.139 |
|
| \begin{align*}
f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
3.437 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y+b \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
66.390 |
|
| \begin{align*}
{y^{\prime }}^{2}+y^{2}-a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.749 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{3}+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.111 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y^{3}+a y+b&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.531 |
|
| \begin{align*}
{y^{\prime }}^{2}+a^{2} y^{2} \left (\ln \left (y\right )^{2}-1\right )&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.456 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
30.715 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.445 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y^{\prime }+b y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.258 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x -2\right ) y^{\prime }-y+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.549 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (x +a \right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.534 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (x +1\right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.484 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.720 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.504 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }-b \,x^{2}-c&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.555 |
|
| \begin{align*}
{y^{\prime }}^{2}+a x y^{\prime }+b y+c \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✗ |
✓ |
✗ |
81.808 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (a x +b \right ) y^{\prime }-a y+c&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.581 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
14.286 |
|
| \begin{align*}
{y^{\prime }}^{2}+a \,x^{3} y^{\prime }-2 a \,x^{2} y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.586 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (y^{\prime }-y\right ) {\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.190 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }-2 x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
23.918 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (4 y+1\right ) y^{\prime }+\left (4 y+1\right ) y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.357 |
|
| \begin{align*}
{y^{\prime }}^{2}+a y y^{\prime }-b x -c&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
62.069 |
|
| \begin{align*}
{y^{\prime }}^{2}+\left (b x +a y\right ) y^{\prime }+a b x y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.793 |
|
| \begin{align*}
{y^{\prime }}^{2}-x y y^{\prime }+y^{2} \ln \left (a y\right )&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✗ |
1.793 |
|
| \begin{align*}
{y^{\prime }}^{2}+2 y y^{\prime } \cot \left (x \right )-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.283 |
|
| \begin{align*}
{y^{\prime }}^{2}+y \left (-x +y\right ) y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.530 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 x^{3} y^{2} y^{\prime }-4 x^{2} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
43.134 |
|
| \begin{align*}
{y^{\prime }}^{2}-3 x y^{{2}/{3}} y^{\prime }+9 y^{{5}/{3}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
1.440 |
|
| \begin{align*}
2 {y^{\prime }}^{2}+\left (x -1\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.527 |
|
| \begin{align*}
2 {y^{\prime }}^{2}-2 x^{2} y^{\prime }+3 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
2.733 |
|
| \begin{align*}
3 {y^{\prime }}^{2}-2 x y^{\prime }+y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.788 |
|
| \begin{align*}
3 {y^{\prime }}^{2}+4 x y^{\prime }+x^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.720 |
|
| \begin{align*}
a {y^{\prime }}^{2}+b y^{\prime }-y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.231 |
|
| \begin{align*}
a {y^{\prime }}^{2}+b \,x^{2} y^{\prime }+c x y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✗ |
19.558 |
|
| \begin{align*}
a {y^{\prime }}^{2}+y y^{\prime }-x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
51.444 |
|
| \begin{align*}
a {y^{\prime }}^{2}-y y^{\prime }-x&=0 \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
24.312 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.269 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x -2 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
7.416 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y^{\prime }-y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.654 |
|
| \begin{align*}
{y^{\prime }}^{2} x +4 y^{\prime }-2 y&=0 \\
\end{align*} |
[_rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.868 |
|
| \begin{align*}
{y^{\prime }}^{2} x +x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
8.137 |
|