| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
\tan \left (y^{\prime }\right )&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.226 |
|
| \begin{align*}
x^{2} y^{\prime } \cos \left (y\right )+1&=0 \\
y \left (\infty \right ) &= \frac {16 \pi }{3} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✗ |
11.265 |
|
| \begin{align*}
x^{2} y^{\prime }+\cos \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {10 \pi }{3} \\
\end{align*} |
[_separable] |
✗ |
✓ |
✗ |
✗ |
7.723 |
|
| \begin{align*}
x^{3} y^{\prime }-\sin \left (y\right )&=1 \\
y \left (\infty \right ) &= 5 \pi \\
\end{align*} |
[_separable] |
✓ |
✗ |
✗ |
✗ |
5.235 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }-\frac {\cos \left (2 y\right )^{2}}{2}&=0 \\
y \left (-\infty \right ) &= \frac {7 \pi }{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
4.464 |
|
| \begin{align*}
{\mathrm e}^{y}&={\mathrm e}^{4 y} y^{\prime }+1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.496 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=y-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.874 |
|
| \begin{align*}
y^{\prime }&=2 x \left (\pi +y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.658 |
|
| \begin{align*}
x^{2} y^{\prime }+\sin \left (2 y\right )&=1 \\
y \left (\infty \right ) &= \frac {11 \pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
13.454 |
|
| \begin{align*}
y^{\prime } x&=y+x \cos \left (\frac {y}{x}\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
5.636 |
|
| \begin{align*}
x -y+y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.153 |
|
| \begin{align*}
y^{\prime } x&=y \left (\ln \left (y\right )-\ln \left (x \right )\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
9.040 |
|
| \begin{align*}
x^{2} y^{\prime }&=x^{2}-y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.802 |
|
| \begin{align*}
y^{\prime } x&=y+\sqrt {y^{2}-x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.551 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{2}+x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
4.651 |
|
| \begin{align*}
4 x -3 y+\left (-3 x +2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
10.116 |
|
| \begin{align*}
y-x +\left (x +y\right ) y^{\prime }&=0 \\
\end{align*} | [[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 6.965 |
|
| \begin{align*}
x +y-2+\left (1-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.802 |
|
| \begin{align*}
3 y-7 x +7-\left (3 x -7 y-3\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
73.326 |
|
| \begin{align*}
x +y-2+\left (x -y+4\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.364 |
|
| \begin{align*}
x +y+\left (x -y-2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.073 |
|
| \begin{align*}
2 x +3 y-5+\left (3 x +2 y-5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
5.908 |
|
| \begin{align*}
8 x +4 y+1+\left (4 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| \begin{align*}
x -2 y-1+\left (3 x -6 y+2\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
8.007 |
|
| \begin{align*}
x +y+\left (x +y-1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.679 |
|
| \begin{align*}
2 x \left (x -y^{2}\right ) y^{\prime }+y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
5.296 |
|
| \begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.750 |
|
| \begin{align*}
y \left (1+\sqrt {1+x^{2} y^{4}}\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✓ |
✓ |
6.642 |
|
| \begin{align*}
x +y^{3}+3 \left (y^{3}-x \right ) y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
6.821 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{-x} \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
1.665 |
|
| \begin{align*}
x^{2}-y^{\prime } x&=y \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.454 |
|
| \begin{align*}
y^{\prime }-2 y x&=2 x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.937 |
|
| \begin{align*}
y^{\prime }+2 y x&={\mathrm e}^{-x^{2}} \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 2.345 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=2 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.688 |
|
| \begin{align*}
y^{\prime } x -2 y&=\cos \left (x \right ) x^{3} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.464 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=\frac {1}{\cos \left (x \right )^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.536 |
|
| \begin{align*}
x \ln \left (x \right ) y^{\prime }-y&=3 x^{3} \ln \left (x \right )^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.986 |
|
| \begin{align*}
\left (2 x -y^{2}\right ) y^{\prime }&=2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
3.234 |
|
| \begin{align*}
y^{\prime }+y \cos \left (x \right )&=\cos \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.931 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 y \ln \left (y\right )+y-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
4.289 |
|
| \begin{align*}
\left (\frac {{\mathrm e}^{-y^{2}}}{2}-y x \right ) y^{\prime }-1&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.807 |
|
| \begin{align*}
y^{\prime }-{\mathrm e}^{x} y&=2 x \,{\mathrm e}^{{\mathrm e}^{x}} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.126 |
|
| \begin{align*}
y^{\prime }+y x \,{\mathrm e}^{x}&={\mathrm e}^{{\mathrm e}^{x} \left (1-x \right )} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.121 |
|
| \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 ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.838 |
|
| \begin{align*}
y^{\prime }-y&=-2 \,{\mathrm e}^{-x} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.853 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-y \cos \left (x \right )&=-\frac {\sin \left (x \right )^{2}}{x^{2}} \\
y \left (\infty \right ) &= 0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| \begin{align*}
x^{2} y^{\prime } \cos \left (\frac {1}{x}\right )-y \sin \left (\frac {1}{x}\right )&=-1 \\
y \left (\infty \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.641 |
|
| \begin{align*}
2 y^{\prime } x -y&=1-\frac {2}{\sqrt {x}} \\
y \left (\infty \right ) &= -1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✗ |
4.500 |
|
| \begin{align*}
x^{2} y^{\prime }+y&=\left (x^{2}+1\right ) {\mathrm e}^{x} \\
y \left (-\infty \right ) &= 1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✗ |
✓ |
3.222 |
|
| \begin{align*}
y^{\prime } x +y&=2 x \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
4.099 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=1 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.353 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y \sin \left (x \right )&=-\sin \left (2 x \right ) \\
y \left (\frac {\pi }{2}\right ) &= 0 \\
\end{align*} | [_linear] | ✓ | ✓ | ✓ | ✓ | 3.397 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.627 |
|
| \begin{align*}
3 y^{2} y^{\prime } x -2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.913 |
|
| \begin{align*}
\left (x^{3}+{\mathrm e}^{y}\right ) y^{\prime }&=3 x^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.451 |
|
| \begin{align*}
y^{\prime }+3 y x&=y \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.823 |
|
| \begin{align*}
y^{\prime }-2 \,{\mathrm e}^{x} y&=2 \sqrt {{\mathrm e}^{x} y} \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✗ |
9.202 |
|
| \begin{align*}
2 \ln \left (x \right ) y^{\prime }+\frac {y}{x}&=\frac {\cos \left (x \right )}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.340 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+y \cos \left (x \right )&=y^{3} \sin \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.736 |
|
| \begin{align*}
\left (1+x^{2}+y^{2}\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘]] |
✓ |
✓ |
✓ |
✓ |
2.076 |
|
| \begin{align*}
y^{\prime }-y \cos \left (x \right )&=y^{2} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.424 |
|
| \begin{align*}
y^{\prime }-\tan \left (y\right )&=\frac {{\mathrm e}^{x}}{\cos \left (y\right )} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
3.746 |
|
| \begin{align*}
y^{\prime }&=y \left ({\mathrm e}^{x}+\ln \left (y\right )\right ) \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(x)*y+H(x)]‘]] |
✗ |
✓ |
✓ |
✓ |
4.920 |
|
| \begin{align*}
y^{\prime } \cos \left (y\right )+\sin \left (y\right )&=x +1 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
3.975 |
|
| \begin{align*}
y^{\prime } y+1&=\left (x -1\right ) {\mathrm e}^{-\frac {y^{2}}{2}} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✗ |
6.957 |
|
| \begin{align*}
y^{\prime }+x \sin \left (2 y\right )&=2 x \,{\mathrm e}^{-x^{2}} \cos \left (y\right )^{2} \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✗ |
✓ |
✓ |
✗ |
9.950 |
|
| \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] |
✓ |
✓ |
✓ |
✓ |
26.503 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
2.696 |
|
| \begin{align*}
\frac {x}{\sqrt {y^{2}+x^{2}}}+\frac {1}{x}+\frac {1}{y}+\left (\frac {y}{\sqrt {y^{2}+x^{2}}}+\frac {1}{y}-\frac {x}{y^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✗ |
✗ |
8.332 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
8.410 |
|
| \begin{align*}
2 x +\frac {y^{2}+x^{2}}{x^{2} y}&=\frac {\left (y^{2}+x^{2}\right ) y^{\prime }}{x y^{2}} \\
\end{align*} | [[_homogeneous, ‘class D‘], _exact, _rational] | ✓ | ✓ | ✓ | ✗ | 3.868 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
25.052 |
|
| \begin{align*}
3 x^{2}-2 x -y+\left (2 y-x +3 y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
2.459 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
34.829 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
5.944 |
|
| \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] |
✓ |
✓ |
✗ |
✗ |
18.510 |
|
| \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] |
✓ |
✓ |
✓ |
✗ |
14.158 |
|
| \begin{align*}
y \left (a^{2}+x^{2}+y^{2}\right ) y^{\prime }+x \left (y^{2}-a^{2}+x^{2}\right )&=0 \\
\end{align*} |
[_exact, _rational] |
✓ |
✓ |
✓ |
✗ |
3.354 |
|
| \begin{align*}
3 x^{2} y+y^{3}+\left (x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
9.967 |
|
| \begin{align*}
1-x^{2} y+x^{2} \left (y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
3.002 |
|
| \begin{align*}
x^{2}+y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
1.876 |
|
| \begin{align*}
x +y^{2}-2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.772 |
|
| \begin{align*}
2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.102 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.089 |
|
| \begin{align*}
x +\sin \left (x \right )+\sin \left (y\right )+y^{\prime } \cos \left (y\right )&=0 \\
\end{align*} |
[‘y=_G(x,y’)‘] |
✓ |
✓ |
✓ |
✓ |
5.862 |
|
| \begin{align*}
2 x y^{2}-3 y^{3}+\left (7-3 x y^{2}\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational] |
✓ |
✓ |
✓ |
✓ |
3.257 |
|
| \begin{align*}
3 y^{2}-x +\left (2 y^{3}-6 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational] |
✓ |
✓ |
✓ |
✓ |
12.795 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 x y^{\prime } y&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.521 |
|
| \begin{align*}
x -y x +\left (y+x^{2}\right ) y^{\prime }&=0 \\
\end{align*} | [_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class A‘]] | ✓ | ✓ | ✓ | ✓ | 8.306 |
|
| \begin{align*}
4 {y^{\prime }}^{2}-9 x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.641 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } y&=y^{2} \left ({\mathrm e}^{2 x}-1\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.618 |
|
| \begin{align*}
{y^{\prime }}^{2}-2 y^{\prime } x -8 x^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.274 |
|
| \begin{align*}
x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+2 y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
0.156 |
|
| \begin{align*}
{y^{\prime }}^{2}-\left (2 x +y\right ) y^{\prime }+x^{2}+y x&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.234 |
|
| \begin{align*}
{y^{\prime }}^{3}+\left (2+x \right ) {\mathrm e}^{y}&=0 \\
\end{align*} |
[[_1st_order, _with_exponential_symmetries]] |
✓ |
✓ |
✓ |
✗ |
58.571 |
|
| \begin{align*}
{y^{\prime }}^{3}&=y {y^{\prime }}^{2}-x^{2} y^{\prime }+x^{2} y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.448 |
|
| \begin{align*}
{y^{\prime }}^{2}-y^{\prime } y+{\mathrm e}^{x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.737 |
|
| \begin{align*}
{y^{\prime }}^{2}-4 y^{\prime } x +2 y+2 x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘]] |
✓ |
✓ |
✗ |
✓ |
0.977 |
|
| \begin{align*}
y&={y^{\prime }}^{2} {\mathrm e}^{y^{\prime }} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.763 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{\frac {y^{\prime }}{y}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
0.708 |
|