| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
{y^{\prime }}^{2}+y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
3.290 |
|
| \begin{align*}
y^{\prime } y^{\prime \prime }&=a x {y^{\prime }}^{5}+3 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_2nd_order, _missing_y]] |
✗ |
✗ |
✗ |
✗ |
24.498 |
|
| \begin{align*}
2 y^{\prime \prime \prime } y^{\prime }&=2 {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.434 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=3 y^{\prime } {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.573 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) y^{\prime \prime \prime }&=\left (a +3 y^{\prime }\right ) {y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
9.012 |
|
| \begin{align*}
{y^{\prime }}^{3} y^{\prime \prime \prime }&=1 \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
1.715 |
|
| \begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=2 \\
\end{align*} | [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _exact, _nonlinear], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] | ✓ | ✓ | ✓ | ✗ | 0.503 |
|
| \begin{align*}
y^{\prime \prime } y^{\prime \prime \prime }&=a \sqrt {1+b^{2} {y^{\prime \prime }}^{2}} \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✗ |
6.018 |
|
| \begin{align*}
2 x y^{\prime \prime } y^{\prime \prime \prime }&=-a^{2}+{y^{\prime \prime }}^{2} \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
1.036 |
|
| \begin{align*}
1-{y^{\prime \prime }}^{2}+2 x y^{\prime \prime } y^{\prime \prime \prime }+\left (-x^{2}+1\right ) {y^{\prime \prime \prime }}^{2}&=0 \\
\end{align*} |
[[_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.802 |
|
| \begin{align*}
\sqrt {1+{y^{\prime \prime }}^{2}}\, \left (1-y^{\prime \prime \prime }\right )&=y^{\prime \prime } y^{\prime \prime \prime } \\
\end{align*} |
[[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2]] |
✓ |
✓ |
✓ |
✓ |
5.637 |
|
| \begin{align*}
3 y^{\prime \prime } y^{\prime \prime \prime \prime }&=5 {y^{\prime \prime \prime }}^{2} \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries], [_high_order, _reducible, _mu_poly_yn]] |
✓ |
✓ |
✓ |
✗ |
0.955 |
|
| \begin{align*}
40 {y^{\prime \prime \prime }}^{3}-45 y^{\prime \prime } y^{\prime \prime \prime } y^{\prime \prime \prime \prime }+9 {y^{\prime \prime }}^{2} y^{\left (5\right )}&=0 \\
\end{align*} |
[[_high_order, _missing_x], [_high_order, _missing_y], [_high_order, _with_linear_symmetries]] |
✗ |
✓ |
✓ |
✗ |
0.082 |
|
| \begin{align*}
y^{\prime }&=\frac {x y}{x^{2}-y^{2}} \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 3.259 |
|
| \begin{align*}
y^{\prime }&=\frac {-3+x +y}{x -y-1} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
11.585 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y-1}{4 x +2 y+5} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
4.813 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x +1}&=\left (x +1\right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.859 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.464 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.249 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.494 |
|
| \begin{align*}
y^{2} \left (1+{y^{\prime }}^{2}\right )&=R^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.711 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
6.210 |
|
| \begin{align*}
y&=x {y^{\prime }}^{2}+{y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.444 |
|
| \begin{align*}
x \left (1-y\right ) y^{\prime }+\left (x +1\right ) y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
1.971 |
|
| \begin{align*}
y^{2}+x y^{2}+\left (x^{2}-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.598 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.641 |
|
| \begin{align*}
1+y^{2}-\left (y+\sqrt {1+y^{2}}\right ) \left (x^{2}+1\right )^{{3}/{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.776 |
|
| \begin{align*}
\cos \left (y\right ) \sin \left (x \right )-\cos \left (x \right ) \sin \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.615 |
|
| \begin{align*}
\sec \left (x \right )^{2} \tan \left (y\right )+\sec \left (y\right )^{2} \tan \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.371 |
|
| \begin{align*}
\left (y-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.814 |
|
| \begin{align*}
\left (2 \sqrt {y x}-x \right ) y^{\prime }+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.751 |
|
| \begin{align*}
y^{\prime } x -y-\sqrt {y^{2}+x^{2}}&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 4.897 |
|
| \begin{align*}
x -y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.744 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.846 |
|
| \begin{align*}
2 x -y+1+\left (-1+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✗ |
13.442 |
|
| \begin{align*}
3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
64.977 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{x^{2}+1}&=\frac {1}{2 x \left (x^{2}+1\right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.377 |
|
| \begin{align*}
x \left (-x^{2}+1\right ) y^{\prime }+\left (2 x^{2}-1\right ) y&=a \,x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.934 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{{3}/{2}}}&=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.276 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )&=\frac {\sin \left (2 x \right )}{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.227 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y&=\arctan \left (x \right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.141 |
|
| \begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-x z&=a x z^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.769 |
|
| \begin{align*}
3 z^{2} z^{\prime }-a z^{3}&=x +1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.692 |
|
| \begin{align*}
z^{\prime }+2 x z&=2 a \,x^{3} z^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.701 |
|
| \begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.079 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
x^{3}+3 x y^{2}+\left (y^{3}+3 x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.162 |
|
| \begin{align*}
1+\frac {y^{2}}{x^{2}}-\frac {2 y y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.283 |
|
| \begin{align*}
\frac {3 x}{y^{3}}+\left (\frac {1}{y^{2}}-\frac {3 x^{2}}{y^{4}}\right ) y^{\prime }&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✓ | 0.303 |
|
| \begin{align*}
x +y^{\prime } y+\frac {x y^{\prime }}{y^{2}+x^{2}}-\frac {y}{y^{2}+x^{2}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
0.165 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.195 |
|
| \begin{align*}
{\mathrm e}^{x} \left (x^{2}+y^{2}+2 x \right )+2 y \,{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.287 |
|
| \begin{align*}
n \cos \left (n x +m y\right )-m \sin \left (m x +n y\right )+\left (m \cos \left (n x +m y\right )-n \sin \left (m x +n y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.220 |
|
| \begin{align*}
\frac {x}{\sqrt {1+x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {1+x^{2}+y^{2}}}+\frac {y}{y^{2}+x^{2}}-\frac {x y^{\prime }}{y^{2}+x^{2}}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact] |
✓ |
✓ |
✓ |
✗ |
0.318 |
|
| \begin{align*}
2 y x +\left (y^{2}-2 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.270 |
|
| \begin{align*}
\frac {1}{x}+\frac {y^{\prime }}{y}+\frac {2}{y}-\frac {2 y^{\prime }}{x}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
-y+y^{\prime } x&=\sqrt {y^{2}+x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
4.750 |
|
| \begin{align*}
\left (7 x +5 y\right ) y^{\prime }+10 x +8 y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.813 |
|
| \begin{align*}
x^{2}+2 y x -y^{2}+\left (y^{2}+2 y x -x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.991 |
|
| \begin{align*}
y^{2}+\left (x^{2}+y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
45.086 |
|
| \begin{align*}
\left (x \cos \left (\frac {y}{x}\right )+\sin \left (\frac {y}{x}\right ) y\right ) y+\left (x \cos \left (\frac {y}{x}\right )-\sin \left (\frac {y}{x}\right ) y\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.303 |
|
| \begin{align*}
\left (y^{2} x^{2}+y x \right ) y+\left (y^{2} x^{2}-1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
0.326 |
|
| \begin{align*}
\left (x^{3} y^{3}+y^{2} x^{2}+y x +1\right ) y+\left (x^{3} y^{3}-y^{2} x^{2}-y x +1\right ) x y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
2 y^{\prime } y+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.295 |
|
| \begin{align*}
x^{2}+y^{2}-2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.302 |
|
| \begin{align*}
2 y x +\left (y^{2}-3 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _rational, _dAlembert] | ✓ | ✓ | ✓ | ✗ | 0.154 |
|
| \begin{align*}
y+\left (-x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.260 |
|
| \begin{align*}
y^{\prime } x -a y+y^{2}&=x^{-2 a} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
0.832 |
|
| \begin{align*}
y^{\prime } x -a y+y^{2}&=x^{-\frac {2 a}{3}} \\
\end{align*} |
[_rational, _Riccati] |
✓ |
✓ |
✓ |
✗ |
3.910 |
|
| \begin{align*}
u^{\prime }+u^{2}&=\frac {c}{x^{{4}/{3}}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.310 |
|
| \begin{align*}
u^{\prime }+b u^{2}&=\frac {c}{x^{4}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
0.273 |
|
| \begin{align*}
u^{\prime }-u^{2}&=\frac {2}{x^{{8}/{3}}} \\
\end{align*} |
[_rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✗ |
0.480 |
|
| \begin{align*}
\frac {\sqrt {f \,x^{4}+c \,x^{3}+c \,x^{2}+b x +a}\, y^{\prime }}{\sqrt {a +b y+c y^{2}+c y^{3}+f y^{4}}}&=-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.562 |
|
| \begin{align*}
{y^{\prime }}^{2}-5 y^{\prime }+6&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.139 |
|
| \begin{align*}
{y^{\prime }}^{2}-\frac {a^{2}}{x^{2}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.161 |
|
| \begin{align*}
{y^{\prime }}^{2}&=\frac {1-x}{x} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.258 |
|
| \begin{align*}
{y^{\prime }}^{2}+\frac {2 x y^{\prime }}{y}-1&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| \begin{align*}
y&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.856 |
|
| \begin{align*}
x&=a y^{\prime }+b {y^{\prime }}^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.211 |
|
| \begin{align*}
y&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.806 |
|
| \begin{align*}
x&=\sqrt {1+{y^{\prime }}^{2}}+a y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.517 |
|
| \begin{align*}
y^{\prime }-\frac {\sqrt {1+{y^{\prime }}^{2}}}{x}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.167 |
|
| \begin{align*}
x^{2} \left (1+{y^{\prime }}^{2}\right )^{3}-a^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.532 |
|
| \begin{align*}
1+{y^{\prime }}^{2}&=\frac {\left (x +a \right )^{2}}{2 a x +x^{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.308 |
|
| \begin{align*}
y&=y^{\prime } x +y^{\prime }-{y^{\prime }}^{2} \\
\end{align*} | [[_1st_order, _with_linear_symmetries], _Clairaut] | ✓ | ✓ | ✓ | ✓ | 0.208 |
|
| \begin{align*}
y&=y^{\prime } x +\sqrt {b^{2}-a^{2} {y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.769 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.011 |
|
| \begin{align*}
y&=y^{\prime } x +a x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.656 |
|
| \begin{align*}
x -y^{\prime } y&=a {y^{\prime }}^{2} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.553 |
|
| \begin{align*}
y^{\prime } y+x&=a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.002 |
|
| \begin{align*}
y^{\prime } y&=x +y^{2}-y^{2} {y^{\prime }}^{2} \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
0.516 |
|
| \begin{align*}
y-\frac {1}{\sqrt {1+{y^{\prime }}^{2}}}&=x +\frac {y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.918 |
|
| \begin{align*}
y-2 y^{\prime } x&=x {y^{\prime }}^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
0.619 |
|
| \begin{align*}
\frac {y-y^{\prime } x}{y^{\prime }+y^{2}}&=\frac {y-y^{\prime } x}{1+x^{2} y^{\prime }} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.563 |
|
| \begin{align*}
2 y x +\left (y^{2}+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
4.080 |
|
| \begin{align*}
\left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
76.248 |
|
| \begin{align*}
x +y-\left (x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
y^{\prime } x -y-x \sin \left (\frac {y}{x}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \begin{align*}
2 x^{2} y+y^{3}+\left (x y^{2}-2 x^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| \begin{align*}
y^{2}+\left (x \sqrt {y^{2}-x^{2}}-y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
19.661 |
|