| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=\frac {y}{2 \ln \left (y\right ) y+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
3.043 |
|
| \begin{align*}
x \left (x -1\right ) y^{\prime }+y&=x^{2} \left (2 x -1\right ) \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.800 |
|
| \begin{align*}
y^{\prime }-y \tan \left (x \right )&=\sec \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.415 |
|
| \begin{align*}
\cos \left (y\right ) y^{\prime }+\sin \left (y\right )&=x +1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.404 |
|
| \begin{align*}
y^{\prime }+\sin \left (y\right )+x \cos \left (y\right )+x&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
4.624 |
|
| \begin{align*}
y^{\prime }-\frac {n y}{x +1}&={\mathrm e}^{x} \left (x +1\right )^{n} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.526 |
|
| \begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
16.284 |
|
| \begin{align*}
y^{\prime }-2 y x&=\cos \left (x \right )-2 x \sin \left (x \right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✓ |
✗ |
✓ |
9.645 |
|
| \begin{align*}
2 \sqrt {x}\, y^{\prime }-y&=-\sin \left (\sqrt {x}\right )-\cos \left (\sqrt {x}\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[_linear] |
✗ |
✓ |
✗ |
✓ |
11.652 |
|
| \begin{align*}
y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \\
y \left (\infty \right ) &= y_{0} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✗ |
✓ |
✗ |
✓ |
11.688 |
|
| \begin{align*}
2 x^{2} y^{\prime }-y x&=2 x \cos \left (x \right )-2 \sin \left (x \right ) \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✗ |
✓ |
✓ |
✗ |
5.767 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
5.704 |
|
| \begin{align*}
\left (x^{2}+1\right ) \ln \left (x^{2}+1\right ) y^{\prime }-2 y x&=\ln \left (x^{2}+1\right )-2 x \arctan \left (x \right ) \\
y \left (-\infty \right ) &= -\frac {\pi }{2} \\
\end{align*} |
[_linear] |
✗ |
✓ |
✓ |
✓ |
52.217 |
|
| \begin{align*}
y^{\prime }-y \,{\mathrm e}^{x}&=\frac {\sin \left (\frac {1}{x}\right )}{x^{2}}-{\mathrm e}^{x} \cos \left (\frac {1}{x}\right ) \\
y \left (-\infty \right ) &= 2 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
16.740 |
|
| \begin{align*}
y^{\prime }-y \ln \left (x \right )&=-\left (2 \ln \left (x \right )+1\right ) x^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.850 |
|
| \begin{align*}
x \left (2 x^{2}+y^{2}\right )+y \left (x^{2}+2 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
17.671 |
|
| \begin{align*}
3 x^{2}+6 x y^{2}+\left (6 x^{2} y+4 y^{3}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.262 |
|
| \begin{align*}
\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {x^{2}+y^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
8.071 |
|
| \begin{align*}
3 x^{2} \tan \left (y\right )-\frac {2 y^{3}}{x^{3}}+\left (x^{3} \sec \left (y\right )^{2}+4 y^{3}+\frac {3 y^{2}}{x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
16.411 |
|
| \begin{align*}
2 x +\frac {x^{2}+y^{2}}{x^{2} y}&=\frac {\left (x^{2}+y^{2}\right ) y^{\prime }}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.229 |
|
| \begin{align*}
\frac {\sin \left (2 x \right )}{y}+x +\left (y-\frac {\sin \left (x \right )^{2}}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
26.297 |
|
| \begin{align*}
3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.094 |
|
| \begin{align*}
\frac {x y}{\sqrt {x^{2}+1}}+2 y x -\frac {y}{x}+\left (\sqrt {x^{2}+1}+x^{2}-\ln \left (x \right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
30.147 |
|
| \begin{align*}
\frac {x}{\sqrt {x^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {x^{2}+y^{2}}}+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
4.790 |
|
| \begin{align*}
\sin \left (y\right )+y \sin \left (x \right )+\frac {1}{x}+\left (x \cos \left (y\right )-\cos \left (x \right )+\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
5.205 |
|
| \begin{align*}
\frac {y+\sin \left (x \right ) \cos \left (y x \right )^{2}}{\cos \left (y x \right )^{2}}+\left (\frac {x}{\cos \left (y x \right )^{2}}+\sin \left (y\right )\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
13.574 |
|
| \begin{align*}
\frac {2 x}{y^{3}}+\frac {\left (y^{2}-3 x^{2}\right ) y^{\prime }}{y^{4}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✗ |
✗ |
23.904 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
3.836 |
|
| \begin{align*}
\frac {x}{\sqrt {\left (x^{2}+y^{2}\right ) \left (1-x^{2}-y^{2}\right )}}+\frac {y y^{\prime }}{\sqrt {\left (x^{2}+y^{2}\right ) \left (1-x^{2}-y^{2}\right )}}+\left (\frac {1}{y \sqrt {y^{2}-x^{2}}}+\frac {{\mathrm e}^{\frac {x}{y}}}{y^{2}}\right ) y-x \left (\frac {1}{y \sqrt {y^{2}-x^{2}}}+\frac {{\mathrm e}^{\frac {x}{y}}}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
89.399 |
|
| \begin{align*}
\frac {\sin \left (\frac {x}{y}\right )}{y}-\frac {y \cos \left (\frac {y}{x}\right )}{x^{2}}+1+\left (\frac {\cos \left (\frac {y}{x}\right )}{x}-\frac {x \sin \left (\frac {x}{y}\right )}{y^{2}}+\frac {1}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
10.207 |
|
| \begin{align*}
y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (-a^{2}+x^{2}+y^{2}\right )&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.482 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.447 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
4.007 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.735 |
|
| \begin{align*}
x +y y^{\prime }+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.819 |
|
| \begin{align*}
x^{2}+y-x y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
1.868 |
|
| \begin{align*}
x +y^{2}-2 x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.592 |
|
| \begin{align*}
2 x^{2} y+2 y+5+\left (2 x^{2}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
2.162 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.372 |
|
| \begin{align*}
x +\sin \left (x \right )+\sin \left (y\right )+\cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
4.711 |
|
| \begin{align*}
2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
2.674 |
|
| \begin{align*}
3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
9.014 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.395 |
|
| \begin{align*}
{y^{\prime }}^{2} x +2 x y^{\prime }-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.572 |
|
| \begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.783 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y y^{\prime }&=y^{2} \left ({\mathrm e}^{x}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.613 |
|
| \begin{align*}
{y^{\prime }}^{2} x^{2}+3 x y y^{\prime }+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.410 |
|
| \begin{align*}
{y^{\prime }}^{2} x -2 y y^{\prime }+x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.593 |
|
| \begin{align*}
\left (x^{2}-2 y x \right ) {y^{\prime }}^{2}-2 x y y^{\prime }+y^{2}-2 y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
98.398 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (x +2\right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
223.964 |
|
| \begin{align*}
{y^{\prime }}^{3}-y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.461 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.007 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {x y^{\prime }}{y}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
8.436 |
|
| \begin{align*}
x&=\ln \left (y^{\prime }\right )+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.934 |
|
| \begin{align*}
x&={y^{\prime }}^{2}-2 y^{\prime }+2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.299 |
|
| \begin{align*}
y&=y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.679 |
|
| \begin{align*}
y&=\arcsin \left (y^{\prime }\right )+\ln \left (1+{y^{\prime }}^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.341 |
|
| \begin{align*}
y&=\left (y^{\prime }-1\right ) {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.872 |
|
| \begin{align*}
{y^{\prime }}^{2} x&={\mathrm e}^{\frac {1}{y^{\prime }}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.617 |
|
| \begin{align*}
\left (1+{y^{\prime }}^{2}\right ) x&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
x \left (1+{y^{\prime }}^{2}\right )^{{3}/{2}}&=a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.135 |
|
| \begin{align*}
y^{{2}/{5}}+{y^{\prime }}^{{2}/{5}}&=a^{{2}/{5}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.016 |
|
| \begin{align*}
y^{4}-{y^{\prime }}^{4}-y {y^{\prime }}^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.106 |
|
| \begin{align*}
x&=\sin \left (y^{\prime }\right )+y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.289 |
|
| \begin{align*}
y&=y^{\prime } \left (1+y^{\prime } \cos \left (y^{\prime }\right )\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
1.747 |
|
| \begin{align*}
2 y&=x y^{\prime }+y^{\prime } \ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
3.690 |
|
| \begin{align*}
y&=2 x y^{\prime }+\ln \left (y^{\prime }\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.598 |
|
| \begin{align*}
y&=x \left (y^{\prime }+1\right )+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
1.157 |
|
| \begin{align*}
y&=2 x y^{\prime }+\sin \left (y^{\prime }\right ) \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
1.170 |
|
| \begin{align*}
y&={y^{\prime }}^{2} x -\frac {1}{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
94.456 |
|
| \begin{align*}
y&=\frac {3 x y^{\prime }}{2}+{\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_dAlembert] |
✓ |
✓ |
✓ |
✗ |
2.034 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {a}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
1.116 |
|
| \begin{align*}
y&=x y^{\prime }+{y^{\prime }}^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✓ |
0.416 |
|
| \begin{align*}
{y^{\prime }}^{2} x -y y^{\prime }-y^{\prime }+1&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.456 |
|
| \begin{align*}
y&=x y^{\prime }+a \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
2.046 |
|
| \begin{align*}
y&=x y^{\prime }+\frac {a y^{\prime }}{\sqrt {1+{y^{\prime }}^{2}}} \\
\end{align*} |
[_Clairaut] |
✓ |
✓ |
✓ |
✗ |
19.556 |
|
| \begin{align*}
x&=\frac {y}{y^{\prime }}+\frac {1}{{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Clairaut] |
✓ |
✓ |
✓ |
✗ |
0.883 |
|
| \begin{align*}
y-y^{3}+\left (2 x y^{2}-x -a y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
4.781 |
|
| \begin{align*}
y^{\prime }&=\left (x -y\right )^{2}+1 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
2.404 |
|
| \begin{align*}
x \sin \left (x \right ) y^{\prime }+\left (\sin \left (x \right )-x \cos \left (x \right )\right ) y&=\sin \left (x \right ) \cos \left (x \right )-x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
7.911 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.550 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
63.154 |
|
| \begin{align*}
5 y x -4 y^{2}-6 x^{2}+\left (y^{2}-2 y x +6 x^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.979 |
|
| \begin{align*}
3 x y^{2}-x^{2}+\left (3 x^{2} y-6 y^{2}-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.485 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+x y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.155 |
|
| \begin{align*}
2 x y \,{\mathrm e}^{x^{2}}-x \sin \left (x \right )+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.972 |
|
| \begin{align*}
2 y^{\prime }+y^{2}+\frac {1}{x^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Riccati, _special]] |
✓ |
✓ |
✓ |
✓ |
3.220 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{2 x -y^{2}} \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
2.229 |
|
| \begin{align*}
x^{2}+x y^{\prime }&=3 x +y^{\prime } \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.561 |
|
| \begin{align*}
4 x^{3} y^{2}+\left (x^{4}-2 x^{4} y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
35.513 |
|
| \begin{align*}
x y y^{\prime }-y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.818 |
|
| \begin{align*}
2 y^{2}-y x -\left (x^{2}-y x +y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
38.037 |
|
| \begin{align*}
\left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.413 |
|
| \begin{align*}
x -y+3+\left (3 x +y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
17.414 |
|
| \begin{align*}
y^{\prime }+\cos \left (\frac {x}{2}+\frac {y}{2}\right )&=\cos \left (\frac {x}{2}-\frac {y}{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.983 |
|
| \begin{align*}
y^{\prime } \left (3 x^{2}-2 x \right )-y \left (6 x -2\right )+\frac {18 x -8}{x}&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \begin{align*}
x y^{2} y^{\prime }-y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.259 |
|
| \begin{align*}
y^{\prime }&=\tan \left (a x +b y+c \right ) \\
\end{align*} |
[[_homogeneous, ‘class C‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.321 |
|
| \begin{align*}
1+{\mathrm e}^{\frac {x}{y}}+{\mathrm e}^{\frac {x}{y}} \left (1-\frac {x}{y}\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
12.459 |
|
| \begin{align*}
x^{2}+y^{2}-x y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.799 |
|