| # |
ODE |
CAS classification |
Solved? |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }-y&=\sin \left (x \right )+\cos \left (2 x \right ) \\
\end{align*} |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
2.296 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x}+1 \\
\end{align*} |
[[_3rd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.141 |
|
| \begin{align*}
y^{\prime \prime \prime }+y^{\prime }&=\sec \left (x \right ) \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✓ |
0.382 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=\frac {{\mathrm e}^{x}}{1+{\mathrm e}^{-x}} \\
\end{align*} |
[[_3rd_order, _missing_y]] |
✓ |
✓ |
✓ |
✗ |
0.273 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.431 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.288 |
|
| \begin{align*}
x^{\prime \prime }+4 x&=\sin \left (2 t \right )^{2} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.576 |
|
| \begin{align*}
t^{2} N^{\prime \prime }-2 t N^{\prime }+2 N&=t \ln \left (t \right ) \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
2.243 |
|
| \begin{align*}
y^{\prime }+\frac {4 y}{x}&=x^{4} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
3.022 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }&=5 x \\
\end{align*} |
[[_high_order, _quadrature]] |
✓ |
✓ |
✓ |
✓ |
0.109 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=\frac {{\mathrm e}^{x}}{x^{5}} \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.435 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sec \left (x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{3 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
y^{\prime \prime }-60 y^{\prime }-900 y&=5 \,{\mathrm e}^{10 x} \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y^{\prime \prime }-7 y^{\prime }&=-3 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.129 |
|
| \begin{align*}
y^{\prime \prime }+\frac {y^{\prime }}{x}-\frac {y}{x^{2}}&=\ln \left (x \right ) \\
\end{align*} |
[[_2nd_order, _exact, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
2.670 |
|
| \begin{align*}
x^{2} y^{\prime \prime }-y^{\prime } x&={\mathrm e}^{x} x^{3} \\
\end{align*} | [[_2nd_order, _missing_y]] | ✓ | ✓ | ✓ | ✓ | 0.563 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=x^{2} \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
2.395 |
|
| \begin{align*}
2 y+y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.229 |
|
| \begin{align*}
2 y+y^{\prime }&=2 \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.133 |
|
| \begin{align*}
2 y+y^{\prime }&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_linear, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.216 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.129 |
|
| \begin{align*}
y^{\prime \prime }-y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime \prime }-y&={\mathrm e}^{x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.233 |
|
| \begin{align*}
y^{\prime \prime }+2 y^{\prime }-3 y&=\sin \left (2 x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.296 |
|
| \begin{align*}
y^{\prime \prime }+y&=\sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.264 |
|
| \begin{align*}
y^{\prime \prime }+y^{\prime }+y&=0 \\
y \left (0\right ) &= 4 \\
y^{\prime }\left (0\right ) &= -3 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.236 |
|
| \begin{align*}
5 y+2 y^{\prime }+y^{\prime \prime }&=3 \,{\mathrm e}^{-2 x} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y^{\prime \prime }+5 y^{\prime }-3 y&=\operatorname {Heaviside}\left (x -4\right ) \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
1.964 |
|
| \begin{align*}
y^{\prime \prime \prime }-y&=5 \\
y \left (0\right ) &= 0 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.329 |
|
| \begin{align*}
y^{\prime \prime \prime \prime }-y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 0 \\
y^{\prime \prime }\left (0\right ) &= 0 \\
y^{\prime \prime \prime }\left (0\right ) &= 0 \\
\end{align*} Using Laplace transform method. |
[[_high_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.303 |
|
| \begin{align*}
y^{\prime \prime \prime }-3 y^{\prime \prime }+3 y^{\prime }-y&={\mathrm e}^{x} x^{2} \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= 2 \\
y^{\prime \prime }\left (0\right ) &= 3 \\
\end{align*} Using Laplace transform method. |
[[_3rd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.291 |
|
| \begin{align*}
x^{\prime \prime }+4 x^{\prime }+4 x&=0 \\
x \left (0\right ) &= 2 \\
x^{\prime }\left (0\right ) &= -2 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|
| \begin{align*}
q^{\prime \prime }+9 q^{\prime }+14 q&=\frac {\sin \left (t \right )}{2} \\
q \left (0\right ) &= 0 \\
q^{\prime }\left (0\right ) &= 1 \\
\end{align*} Using Laplace transform method. |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.316 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime \prime }+\frac {y^{\prime }}{x}+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.616 |
|
| \begin{align*}
x^{3} y^{\prime \prime }+y&=0 \\
\end{align*} Series expansion around \(x=0\). | [[_Emden, _Fowler]] | ✗ | ✗ | ✓ | ✗ | 0.109 |
|
| \begin{align*}
y^{\prime \prime }+y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.278 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x -2 y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.376 |
|
| \begin{align*}
y^{\prime \prime }+x^{2} y^{\prime }+2 y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.373 |
|
| \begin{align*}
y^{\prime \prime }-x^{2} y^{\prime }-y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.421 |
|
| \begin{align*}
y^{\prime \prime }+2 x^{2} y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.290 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x -y&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _exact, _linear, _homogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.379 |
|
| \begin{align*}
y^{\prime \prime }-y x&=0 \\
\end{align*} Series expansion around \(x=0\). |
[[_Emden, _Fowler]] |
✓ |
✓ |
✓ |
✓ |
0.277 |
|
| \begin{align*}
y^{\prime \prime }-2 y^{\prime } x +x^{2} y&=0 \\
y \left (0\right ) &= 1 \\
y^{\prime }\left (0\right ) &= -1 \\
\end{align*} Series expansion around \(x=0\). |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.377 |
|
| \begin{align*}
y^{\prime } x&=2 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.133 |
|
| \begin{align*}
y^{\prime } y+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.546 |
|
| \begin{align*}
y&=y^{\prime } x +{y^{\prime }}^{4} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Clairaut] |
✓ |
✓ |
✓ |
✗ |
3.150 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.855 |
|
| \begin{align*}
y-2 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.239 |
|
| \begin{align*}
\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y&=0 \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✗ |
0.922 |
|
| \begin{align*}
y^{\prime \prime }-y&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
1.282 |
|
| \begin{align*}
y^{\prime \prime }-y&=4-x \\
\end{align*} |
[[_2nd_order, _with_linear_symmetries]] |
✓ |
✓ |
✓ |
✓ |
0.284 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=0 \\
\end{align*} |
[[_2nd_order, _missing_x]] |
✓ |
✓ |
✓ |
✓ |
0.175 |
|
| \begin{align*}
2 y-3 y^{\prime }+y^{\prime \prime }&=2 \,{\mathrm e}^{x} \left (1-x \right ) \\
\end{align*} |
[[_2nd_order, _linear, _nonhomogeneous]] |
✓ |
✓ |
✓ |
✓ |
0.346 |
|
| \begin{align*}
4 y+y^{\prime } x&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.108 |
|
| \begin{align*}
1+2 y+\left (-x^{2}+4\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.572 |
|
| \begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.369 |
|
| \begin{align*}
1+y-\left (x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.574 |
|
| \begin{align*}
x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.497 |
|
| \begin{align*}
x \sin \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )+x \cos \left (\frac {y}{x}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
✓ |
✓ |
5.228 |
|
| \begin{align*}
y^{2} \left (x^{2}+2\right )+\left (x^{3}+y^{3}\right ) \left (y-y^{\prime } x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational] |
✓ |
✓ |
✓ |
✗ |
2.807 |
|
| \begin{align*}
y \sqrt {y^{2}+x^{2}}-x \left (x +\sqrt {y^{2}+x^{2}}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _dAlembert] |
✓ |
✓ |
✓ |
✗ |
14.703 |
|
| \begin{align*}
x +y+1+\left (2 x +2 y+1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
6.865 |
|
| \begin{align*}
1+2 y-\left (4-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.168 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.152 |
|
| \begin{align*}
x +2 y+\left (2 x +3 y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
7.242 |
|
| \begin{align*}
2 y^{\prime } x -2 y&=\sqrt {x^{2}+4 y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _dAlembert] |
✓ |
✓ |
✓ |
✓ |
11.149 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
77.967 |
|
| \begin{align*}
x y^{\prime } y&=\left (1+y\right ) \left (1-x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.612 |
|
| \begin{align*}
y^{2}-x^{2}+x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.424 |
|
| \begin{align*}
y \left (2 y x +1\right )+x \left (-y x +1\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
✓ |
✓ |
7.259 |
|
| \begin{align*}
1+\left (-x^{2}+1\right ) \cot \left (y\right ) y^{\prime }&=0 \\
\end{align*} | [_separable] | ✓ | ✓ | ✓ | ✓ | 3.591 |
|
| \begin{align*}
x^{3}+y^{3}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.441 |
|
| \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‘]] |
✓ |
✓ |
✓ |
✓ |
6.857 |
|
| \begin{align*}
y^{\prime } x +2 y&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.465 |
|
| \begin{align*}
x y^{\prime } y+x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.454 |
|
| \begin{align*}
\cos \left (y\right )+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }&=0 \\
y \left (0\right ) &= \frac {\pi }{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.169 |
|
| \begin{align*}
y^{2}+y x -y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.105 |
|
| \begin{align*}
y^{\prime }&=-2 \left (2 x +3 y\right )^{2} \\
\end{align*} |
[[_homogeneous, ‘class C‘], _Riccati] |
✓ |
✓ |
✓ |
✓ |
10.306 |
|
| \begin{align*}
x -2 \sin \left (y\right )+3+\left (2 x -4 \sin \left (y\right )-3\right ) \cos \left (y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, ‘_with_symmetry_[F(x),G(y)]‘]] |
✓ |
✓ |
✓ |
✓ |
7.634 |
|
| \begin{align*}
x^{2}-y-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.142 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.241 |
|
| \begin{align*}
x +y \cos \left (x \right )+\sin \left (x \right ) y^{\prime }&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.146 |
|
| \begin{align*}
2 x +3 y+4+\left (3 x +4 y+5\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.477 |
|
| \begin{align*}
4 x^{3} y^{3}+\frac {1}{x}+\left (3 x^{4} y^{2}-\frac {1}{y}\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational] |
✓ |
✓ |
✓ |
✓ |
0.833 |
|
| \begin{align*}
2 u^{2}+2 u v+\left (u^{2}+v^{2}\right ) v^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _dAlembert] |
✓ |
✓ |
✓ |
✗ |
0.236 |
|
| \begin{align*}
x \sqrt {y^{2}+x^{2}}-y+\left (y \sqrt {y^{2}+x^{2}}-x \right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.227 |
|
| \begin{align*}
x +y+1-\left (3-x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
0.447 |
|
| \begin{align*}
y^{2}-\frac {y}{x \left (x +y\right )}+2+\left (\frac {1}{x +y}+2 \left (x +1\right ) y\right ) y^{\prime }&=0 \\
\end{align*} | [_exact, _rational] | ✓ | ✓ | ✓ | ✗ | 0.312 |
|
| \begin{align*}
2 x y \,{\mathrm e}^{x^{2} y}+y^{2} {\mathrm e}^{x y^{2}}+1+\left (x^{2} {\mathrm e}^{x^{2} y}+2 x y \,{\mathrm e}^{x y^{2}}-2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact] |
✓ |
✓ |
✓ |
✗ |
0.295 |
|
| \begin{align*}
y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.247 |
|
| \begin{align*}
x y^{\prime } y+x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.841 |
|
| \begin{align*}
x^{2}+y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.663 |
|
| \begin{align*}
1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.451 |
|
| \begin{align*}
x +y+1-\left (-3+x -y\right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
✓ |
✓ |
20.138 |
|
| \begin{align*}
x -x^{2}-y^{2}+y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.550 |
|
| \begin{align*}
2 y-3 x +y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.170 |
|
| \begin{align*}
x -y^{2}+2 x y^{\prime } y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.677 |
|
| \begin{align*}
-y-3 x^{2} \left (y^{2}+x^{2}\right )+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Riccati] |
✓ |
✓ |
✓ |
✓ |
0.276 |
|
| \begin{align*}
y-\ln \left (x \right )-y^{\prime } x&=0 \\
\end{align*} |
[_linear] |
✓ |
✓ |
✓ |
✓ |
0.199 |
|