| # |
ODE |
CAS classification |
Solved |
Maple |
Mma |
Sympy |
time(sec) |
| \begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.783 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
3.355 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
40.514 |
|
| \begin{align*}
y y^{\prime }&=-1+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \begin{align*}
y y^{\prime }&=-1+x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.968 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.006 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.502 |
|
| \begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.059 |
|
| \begin{align*}
y^{3} y^{\prime }&=\left (1+y^{4}\right ) \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.348 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.898 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.343 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.320 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (a \right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.694 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.286 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.030 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.547 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.789 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.668 |
|
| \begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.404 |
|
| \begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.017 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.200 |
|
| \begin{align*}
y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.636 |
|
| \begin{align*}
2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.571 |
|
| \begin{align*}
y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.496 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.684 |
|
| \begin{align*}
3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.928 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.082 |
|
| \begin{align*}
x^{\prime }&=x-x^{2} \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.425 |
|
| \begin{align*}
x^{\prime }&=10 x-x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.210 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 8 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.384 |
|
| \begin{align*}
x^{\prime }&=3 x \left (5-x\right ) \\
x \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.205 |
|
| \begin{align*}
x^{\prime }&=4 x \left (7-x\right ) \\
x \left (0\right ) &= 11 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.382 |
|
| \begin{align*}
x^{\prime }&=7 x \left (x-13\right ) \\
x \left (0\right ) &= 17 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.454 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.780 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.591 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.956 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \begin{align*}
y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.687 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.840 |
|
| \begin{align*}
4 x y^{2}+y^{\prime }&=5 y^{2} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.033 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.710 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.398 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.803 |
|
| \begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.078 |
|
| \begin{align*}
9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.116 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.717 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.938 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}+2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.313 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}-y}{\tan \left (x \right )} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.493 |
|
| \begin{align*}
y^{\prime }+y^{2}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.219 |
|
| \begin{align*}
y^{\prime }&=2 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.696 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
2.955 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
46.645 |
|
| \begin{align*}
y y^{\prime }&=-1+x \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.027 |
|
| \begin{align*}
y y^{\prime }&=-1+x \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.694 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.493 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.726 |
|
| \begin{align*}
y y^{\prime }&=x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.274 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-16}} \\
y \left (5\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.567 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+3 y^{2} x^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.248 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.921 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.384 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.347 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.027 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.819 |
|
| \begin{align*}
y^{2} y^{\prime }+2 x y^{3}&=6 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.570 |
|
| \begin{align*}
y^{\prime }&=y+y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.000 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=5 y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.031 |
|
| \begin{align*}
y^{\prime } x +6 y&=3 x y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.978 |
|
| \begin{align*}
2 y^{\prime } x +y^{3} {\mathrm e}^{-2 x}&=2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.707 |
|
| \begin{align*}
y^{2} \left (y^{\prime } x +y\right ) \sqrt {x^{4}+1}&=x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.457 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&={\mathrm e}^{-x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.636 |
|
| \begin{align*}
3 y^{2} y^{\prime } x&=3 x^{4}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.165 |
|
| \begin{align*}
x y^{2}+3 y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.138 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.583 |
|
| \begin{align*}
2 x y^{2}+x^{2} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.434 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.887 |
|
| \begin{align*}
y^{\prime } x +2 y&=6 \sqrt {y}\, x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.884 |
|
| \begin{align*}
x^{2} y^{\prime }&=y x +3 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.379 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
54.810 |
|
| \begin{align*}
2 x^{2} y-x^{3} y^{\prime }&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.264 |
|
| \begin{align*}
3 x^{5} y^{2}+x^{3} y^{\prime }&=2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.108 |
|
| \begin{align*}
y^{\prime } x&=6 y+12 x^{4} y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.586 |
|
| \begin{align*}
9 y^{2} x^{2}+x^{{3}/{2}} y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.678 |
|
| \begin{align*}
3 y+x^{3} y^{4}+3 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.924 |
|
| \begin{align*}
y^{\prime }&=x y^{3}-y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.000 |
|
| \begin{align*}
y^{\prime }&=\frac {-3 x^{2}-2 y^{2}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.287 |
|
| \begin{align*}
y^{\prime }&=\cot \left (x \right ) \left (\sqrt {y}-y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.365 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.028 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.566 |
|
| \begin{align*}
\sin \left (x \right ) y^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.691 |
|
| \begin{align*}
y^{\prime }&=\left (1-2 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{6}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.885 |
|
| \begin{align*}
y^{\prime }&=\frac {1-2 x}{y} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.830 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{x} \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.496 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y+x^{2} y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.556 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}}{\sqrt {x^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.355 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right )}{4 y^{3}} \\
y \left (0\right ) &= -\frac {\sqrt {2}}{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.592 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.727 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.888 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.618 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.705 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.446 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-3 y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.774 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-x^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.550 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.678 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.300 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.402 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.634 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.480 |
|
| \begin{align*}
y^{\prime }&=y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.999 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.469 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.909 |
|
| \begin{align*}
y^{\prime }&=-b \sqrt {y}+a y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.626 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.037 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (1+y\right )}{x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.589 |
|
| \begin{align*}
y^{\prime }&=a y^{\frac {a -1}{a}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.442 |
|
| \begin{align*}
y^{\prime } x +y^{2}+y&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.744 |
|
| \begin{align*}
y^{\prime }+x \left (y^{2}+y\right )&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.099 |
|
| \begin{align*}
y^{\prime }&=2 x y \left (1+y^{2}\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
12.365 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.699 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (3\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.603 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
y \left (0\right ) &= \operatorname {y0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.885 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{5}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
14.746 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.300 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
0.528 |
|
| \begin{align*}
7 y^{\prime } x -2 y&=-\frac {x^{2}}{y^{6}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
0.389 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y&=2 \,{\mathrm e}^{\frac {1}{x}} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.891 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+2 y x&=\frac {1}{\left (x^{2}+1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.951 |
|
| \begin{align*}
y^{\prime }-y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.197 |
|
| \begin{align*}
y^{\prime }-\frac {\left (x +1\right ) y}{3 x}&=y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.298 |
|
| \begin{align*}
y^{\prime }-2 y&=x y^{3} \\
y \left (0\right ) &= 2 \sqrt {2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.547 |
|
| \begin{align*}
y^{\prime }-y x&=y^{{3}/{2}} x \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
44.766 |
|
| \begin{align*}
y^{\prime } x +y&=y^{4} x^{4} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.583 |
|
| \begin{align*}
y^{\prime }-2 y&=2 \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.081 |
|
| \begin{align*}
y^{\prime }-4 y&=\frac {48 x}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.685 |
|
| \begin{align*}
x^{2} y^{\prime }+2 y x&=y^{3} \\
y \left (1\right ) &= \frac {\sqrt {2}}{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.710 |
|
| \begin{align*}
y^{\prime }-y&=x \sqrt {y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
1.304 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.323 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}+x^{4} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
104.283 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.820 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.979 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.732 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.468 |
|
| \begin{align*}
y y^{\prime } x&=3 x^{2}+4 y^{2} \\
y \left (1\right ) &= \sqrt {3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.731 |
|
| \begin{align*}
3 y^{2} y^{\prime } x&=y^{3}+x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.046 |
|
| \begin{align*}
y y^{\prime } x&=3 x^{6}+6 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.056 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.811 |
|
| \begin{align*}
\left (y^{3}-1\right ) {\mathrm e}^{x}+3 y^{2} \left ({\mathrm e}^{x}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.693 |
|
| \begin{align*}
{\mathrm e}^{x} \left (y^{2} x^{4}+4 x^{3} y^{2}+1\right )+\left (2 x^{4} y \,{\mathrm e}^{x}+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.931 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.125 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.082 |
|
| \begin{align*}
3 y^{2} x^{2}+2 y+2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.668 |
|
| \begin{align*}
t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.857 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t}{y+t^{2} y} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.459 |
|
| \begin{align*}
\sqrt {t^{2}+1}\, y^{\prime }&=\frac {t y^{3}}{\sqrt {t^{2}+1}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.068 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.847 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.750 |
|
| \begin{align*}
t^{2} \left (1+y^{2}\right )+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.738 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t}{y+t^{2} y} \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.162 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{t}+\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.622 |
|
| \begin{align*}
2 t y y^{\prime }&=3 y^{2}-t^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.484 |
|
| \begin{align*}
y^{\prime }&=\frac {\left (1+\cos \left (4 t \right )\right ) y}{4}-\frac {\left (1-\cos \left (4 t \right )\right ) y^{2}}{800} \\
y \left (0\right ) &= 100 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.444 |
|
| \begin{align*}
y^{\prime }&=t y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
27.250 |
|
| \begin{align*}
y^{\prime }&={\mathrm e}^{t} y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.966 |
|
| \begin{align*}
y^{\prime }&=t y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.480 |
|
| \begin{align*}
x^{\prime }&=x \left (1-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.030 |
|
| \begin{align*}
x^{\prime }&=-x \left (1-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.658 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.690 |
|
| \begin{align*}
x y^{2}+x +\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.257 |
|
| \begin{align*}
x y^{2}+x +\left (x^{2} y-y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.934 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.037 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.263 |
|
| \begin{align*}
y^{2}+y y^{\prime }+x^{2} y y^{\prime }-1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.199 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=0 \\
y \left (3\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.221 |
|
| \begin{align*}
\left (x^{2}+3 x \right ) y^{\prime }&=y^{3}+2 y \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.938 |
|
| \begin{align*}
x^{2}+y^{2}&=y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.035 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.094 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.361 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.110 |
|
| \begin{align*}
y \left (-x^{2}+y\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.885 |
|
| \begin{align*}
{\mathrm e}^{x} y^{\prime }&=2 x y^{2}+{\mathrm e}^{x} y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.796 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+{\mathrm e}^{x} x^{4}-2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.482 |
|
| \begin{align*}
y \left (1-y^{2} x^{4}\right )+y^{\prime } x&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.210 |
|
| \begin{align*}
3 y^{2} y^{\prime }-x y^{3}&={\mathrm e}^{\frac {x^{2}}{2}} \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.401 |
|
| \begin{align*}
y^{3} y^{\prime }+y^{4} x&=x \,{\mathrm e}^{-x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.714 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.798 |
|
| \begin{align*}
y^{\prime }-y x&=\sqrt {y}\, x \,{\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.869 |
|
| \begin{align*}
t x^{\prime }+x \left (1-x^{2} t^{4}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.901 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.521 |
|
| \begin{align*}
y^{\prime }-y x&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.014 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} x^{2} \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.740 |
|
| \begin{align*}
r^{\prime }+\left (r-\frac {1}{r}\right ) \theta &=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.978 |
|
| \begin{align*}
y^{\prime } x +2 y&=3 x^{3} y^{{4}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.368 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.275 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.323 |
|
| \begin{align*}
y+y^{\prime }&=y^{2} {\mathrm e}^{-t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.709 |
|
| \begin{align*}
-y^{\prime } x +y&=2 y^{\prime }+2 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.161 |
|
| \begin{align*}
2 x^{3}-y^{3}-3 x +3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.740 |
|
| \begin{align*}
3 x -6&=y y^{\prime } x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.546 |
|
| \begin{align*}
2 y^{\prime } x -y+\frac {x^{2}}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.984 |
|
| \begin{align*}
y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.581 |
|
| \begin{align*}
y^{\prime } x -5 y-x \sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.520 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.925 |
|
| \begin{align*}
y^{\prime } x -2 y-2 x^{4} y^{3}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.726 |
|
| \begin{align*}
y^{\prime } x +y&=x^{3} y^{6} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.562 |
|
| \begin{align*}
x^{\prime }&=x+x^{2} {\mathrm e}^{\theta } \\
x \left (0\right ) &= 2 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.829 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (2\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.125 |
|
| \begin{align*}
4 x y^{2}+\left (x^{2}+1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.252 |
|
| \begin{align*}
2 \left (x^{2}+1\right ) y^{\prime }&=\left (2 y^{2}-1\right ) x y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.651 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.909 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.410 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{t}}{y} \\
y \left (\ln \left (2\right )\right ) &= -8 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.643 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.602 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.991 |
|
| \begin{align*}
y^{\prime }-x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.697 |
|
| \begin{align*}
x^{2} y^{\prime }+x y^{2}&=4 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.047 |
|
| \begin{align*}
y^{\prime }&=-\frac {2 x^{2}+y^{2}+x}{y x} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.548 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}}{x^{2}}-y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.313 |
|
| \begin{align*}
y^{\prime } x +y-\frac {y^{2}}{x^{{3}/{2}}}&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.922 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.616 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.051 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.244 |
|
| \begin{align*}
y^{\prime }&=\frac {\cos \left (x \right )-2 x y^{2}}{2 x^{2} y} \\
y \left (\pi \right ) &= \frac {1}{\pi } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.272 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x^{2}+1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.743 |
|
| \begin{align*}
y^{\prime }&=y^{3} \sin \left (x \right ) \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
6.983 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {4 x^{2} \cos \left (x \right )}{y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.490 |
|
| \begin{align*}
y^{\prime }+\frac {\tan \left (x \right ) y}{2}&=2 y^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.934 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{2 x}&=6 y^{{1}/{3}} x^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.137 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 \sqrt {x^{2}+1}\, \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.928 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.676 |
|
| \begin{align*}
2 x \left (y^{\prime }+x^{2} y^{3}\right )+y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.625 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) \left (y^{\prime }-\sqrt {y}\right )&=2 \left (b -a \right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.303 |
|
| \begin{align*}
y^{\prime }+\frac {6 y}{x}&=\frac {3 y^{{2}/{3}} \cos \left (x \right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.651 |
|
| \begin{align*}
y^{\prime }+4 y x&=4 x^{3} \sqrt {y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.710 |
|
| \begin{align*}
y^{\prime }-\frac {y}{2 x \ln \left (x \right )}&=2 x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.879 |
|
| \begin{align*}
y^{\prime }-\frac {y}{\left (\pi -1\right ) x}&=\frac {3 x y^{\pi }}{1-\pi } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.080 |
|
| \begin{align*}
2 y^{\prime }+\cot \left (x \right ) y&=\frac {8 \cos \left (x \right )^{3}}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.109 |
|
| \begin{align*}
\left (1-\sqrt {3}\right ) y^{\prime }+y \sec \left (x \right )&=y^{\sqrt {3}} \sec \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.703 |
|
| \begin{align*}
y^{\prime }+\frac {2 x y}{x^{2}+1}&=x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.552 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{3} \sin \left (x \right )^{3} \\
y \left (\frac {\pi }{2}\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.882 |
|
| \begin{align*}
x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.046 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }-y^{2} x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.792 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.728 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.162 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=2 x -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.091 |
|
| \begin{align*}
y^{\prime }&=6 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.234 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.271 |
|
| \begin{align*}
y^{\prime } x&=2 y \left (-1+y\right ) \\
y \left (\frac {1}{2}\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.263 |
|
| \begin{align*}
y \,{\mathrm e}^{2 x} y^{\prime }+2 x&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.025 |
|
| \begin{align*}
y y^{\prime } x&=2 x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.263 |
|
| \begin{align*}
x^{2}-y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.808 |
|
| \begin{align*}
x^{2} y^{\prime }-2 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.843 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (1+y^{2}\right )}{y \left (x^{2}+1\right )} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.109 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.977 |
|
| \begin{align*}
2+y^{2}+2 x +2 y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| \begin{align*}
1-\left (y-2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.479 |
|
| \begin{align*}
3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.267 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.892 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )-y&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.372 |
|
| \begin{align*}
y y^{\prime } x +y^{2}-\sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.029 |
|
| \begin{align*}
2 x^{3}-y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
1.520 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y+y^{2} \cos \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.491 |
|
| \begin{align*}
x y^{2} \left (y^{\prime } x +y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.921 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.855 |
|
| \begin{align*}
{\mathrm e}^{x}+3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.783 |
|
| \begin{align*}
2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.632 |
|
| \begin{align*}
x^{2} \left (-y+y^{\prime } x \right )&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.967 |
|
| \begin{align*}
2 x^{{3}/{2}}+x^{2}+y^{2}+2 y \sqrt {x}\, y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.690 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.655 |
|
| \begin{align*}
x y^{3}-1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.892 |
|
| \begin{align*}
y^{\prime }&=x y \left (3+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.756 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.392 |
|
| \begin{align*}
y^{\prime }&=\left (a +b y \cos \left (k x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.155 |
|
| \begin{align*}
y^{\prime }&=y \left (a +b y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.217 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.835 |
|
| \begin{align*}
y^{\prime }+y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.836 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1+a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.415 |
|
| \begin{align*}
y^{\prime }+2 x y \left (1-a \,x^{2} y^{2}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.388 |
|
| \begin{align*}
y^{\prime }+\left (\tan \left (x \right )+y^{2} \sec \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.384 |
|
| \begin{align*}
y^{\prime }+y^{3} \sec \left (x \right ) \tan \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.562 |
|
| \begin{align*}
y^{\prime }&=\left (\tan \left (x \right )+y^{3} \sec \left (x \right )\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.012 |
|
| \begin{align*}
y^{\prime }&=f \left (x \right ) y+g \left (x \right ) y^{k} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.894 |
|
| \begin{align*}
y^{\prime }+2 y \left (1-x \sqrt {y}\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.276 |
|
| \begin{align*}
y^{\prime } x +\left (-y x +1\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.468 |
|
| \begin{align*}
y^{\prime } x&=\left (-y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.181 |
|
| \begin{align*}
y^{\prime } x&=\left (y x +1\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.483 |
|
| \begin{align*}
y^{\prime } x&=a \,x^{3} \left (-y x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.667 |
|
| \begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.782 |
|
| \begin{align*}
y^{\prime } x +\left (a +b \,x^{n} y\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.951 |
|
| \begin{align*}
y^{\prime } x +\left (1-a y \ln \left (x \right )\right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.488 |
|
| \begin{align*}
y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.478 |
|
| \begin{align*}
y^{\prime } x +y \left (1-x y^{2}\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.263 |
|
| \begin{align*}
y^{\prime } x +y&=a \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.458 |
|
| \begin{align*}
y^{\prime } x +y&=a \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.040 |
|
| \begin{align*}
y^{\prime } x&=a y+b \left (x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.546 |
|
| \begin{align*}
y^{\prime } x&=a y+b \left (-x^{2}+1\right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.917 |
|
| \begin{align*}
y^{\prime } x +2 y&=a \,x^{2 k} y^{k} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.039 |
|
| \begin{align*}
y^{\prime } x&=4 y-4 \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.220 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=a y+b x y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.178 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.740 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }&=\left (1-x y^{3}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.017 |
|
| \begin{align*}
\left (a +x \right ) y^{\prime }&=y \left (1-a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.574 |
|
| \begin{align*}
\left (a -x \right ) y^{\prime }&=y+\left (c x +b \right ) y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.099 |
|
| \begin{align*}
2 y^{\prime } x&=y \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.408 |
|
| \begin{align*}
2 y^{\prime } x +y \left (1+y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.309 |
|
| \begin{align*}
2 y^{\prime } x&=\left (1+x -6 y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.237 |
|
| \begin{align*}
2 \left (x +1\right ) y^{\prime }+2 y+\left (x +1\right )^{4} y^{3}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.780 |
|
| \begin{align*}
3 y^{\prime } x&=\left (2+x y^{3}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.139 |
|
| \begin{align*}
3 y^{\prime } x&=\left (3 y^{3} \ln \left (x \right ) x +1\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.959 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a y+x \right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.384 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +b y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.651 |
|
| \begin{align*}
x^{2} y^{\prime }+\left (x^{2}+y^{2}-x \right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.506 |
|
| \begin{align*}
x^{2} y^{\prime }&=2 y \left (x -y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.615 |
|
| \begin{align*}
x^{2} y^{\prime }&=\left (a x +y^{3} b \right ) y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.804 |
|
| \begin{align*}
x^{2} y^{\prime }+y x +\sqrt {y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.566 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }+x y \left (1-y\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.534 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }&=x y \left (1+a y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.729 |
|
| \begin{align*}
\left (-x^{2}+4\right ) y^{\prime }+4 y&=\left (2+x \right ) y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.221 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.102 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y \left (x -y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.033 |
|
| \begin{align*}
\left (a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.901 |
|
| \begin{align*}
\left (-a^{2}+x^{2}\right ) y^{\prime }+y x +b x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.918 |
|
| \begin{align*}
x \left (a +x \right ) y^{\prime }&=\left (b +c y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.785 |
|
| \begin{align*}
\left (x -a \right ) \left (x -b \right ) y^{\prime }&=c y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.027 |
|
| \begin{align*}
x^{3} y^{\prime }&=y \left (y+x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.989 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (x +1\right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.770 |
|
| \begin{align*}
x^{3} y^{\prime }&=\left (2 x^{2}+y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
69.162 |
|
| \begin{align*}
x^{2} \left (1-x \right ) y^{\prime }&=x \left (-x +2\right ) y-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.862 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (x^{2}-y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.142 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (3 x^{2}+a y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.963 |
|
| \begin{align*}
6 x^{3} y^{\prime }&=4 x^{2} y+\left (1-3 x \right ) y^{4} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.619 |
|
| \begin{align*}
x^{4} y^{\prime }&=\left (x^{3}+y\right ) y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.914 |
|
| \begin{align*}
x^{2} \left (-x^{2}+1\right ) y^{\prime }&=\left (x -3 x^{3} y\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.286 |
|
| \begin{align*}
y^{\prime } \left (a +\cos \left (\frac {x}{2}\right )^{2}\right )&=y \tan \left (\frac {x}{2}\right ) \left (1+a +\cos \left (\frac {x}{2}\right )^{2}-y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
10.595 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.161 |
|
| \begin{align*}
y y^{\prime }+x \,{\mathrm e}^{x^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.158 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.089 |
|
| \begin{align*}
y y^{\prime }&=a x +b y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.882 |
|
| \begin{align*}
y y^{\prime }&=b \cos \left (x +c \right )+a y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.720 |
|
| \begin{align*}
y y^{\prime }&=a x +b x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.914 |
|
| \begin{align*}
y y^{\prime }&=\csc \left (x \right )^{2}-\cot \left (x \right ) y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.616 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.333 |
|
| \begin{align*}
2 y y^{\prime }&=x y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.951 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.329 |
|
| \begin{align*}
y y^{\prime } x&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.063 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.209 |
|
| \begin{align*}
y y^{\prime } x +x^{4}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.259 |
|
| \begin{align*}
y y^{\prime } x&=a \,x^{3} \cos \left (x \right )+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.221 |
|
| \begin{align*}
y y^{\prime } x&=a +b y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.036 |
|
| \begin{align*}
y y^{\prime } x&=a \,x^{n}+b y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.866 |
|
| \begin{align*}
y y^{\prime } x&=\left (x^{2}+1\right ) \left (1-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.375 |
|
| \begin{align*}
2 y y^{\prime } x +1-2 x^{3}-y^{2}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.589 |
|
| \begin{align*}
2 y y^{\prime } x +a +y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.984 |
|
| \begin{align*}
2 y y^{\prime } x&=y^{2}+a x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.294 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.174 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.339 |
|
| \begin{align*}
2 y y^{\prime } x&=4 x^{2} \left (2 x +1\right )+y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.406 |
|
| \begin{align*}
2 y y^{\prime } x +x^{2} \left (a \,x^{3}+1\right )&=6 y^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.490 |
|
| \begin{align*}
2 \left (x +1\right ) y y^{\prime }+2 x -3 x^{2}+y^{2}&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.862 |
|
| \begin{align*}
a x y y^{\prime }&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.143 |
|
| \begin{align*}
a x y y^{\prime }+x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.639 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+x \left (1-y^{2}\right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.072 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y y^{\prime }+2 x^{2}+x y^{2}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.645 |
|
| \begin{align*}
2 x^{2} y y^{\prime }&=x^{2} \left (2 x +1\right )-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.506 |
|
| \begin{align*}
2 \left (x +1\right ) x y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.868 |
|
| \begin{align*}
3 x^{2} y y^{\prime }+1+2 x y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.289 |
|
| \begin{align*}
2 y y^{\prime } x^{3}+a +3 y^{2} x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.105 |
|
| \begin{align*}
x y \left (b \,x^{2}+a \right ) y^{\prime }&=A +B y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.093 |
|
| \begin{align*}
3 x^{4} y y^{\prime }&=1-2 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.164 |
|
| \begin{align*}
3 y^{2} y^{\prime }&=1+x +a y^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.888 |
|
| \begin{align*}
3 y^{2} y^{\prime } x&=2 x -y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.697 |
|
| \begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.243 |
|
| \begin{align*}
x^{2} y^{2} y^{\prime }+1-x +x^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.469 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.873 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.684 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-1-y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.633 |
|
| \begin{align*}
\left (-x^{2}+1\right ) z^{\prime }-z x&=a x z^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.466 |
|
| \begin{align*}
3 z^{2} z^{\prime }-a z^{3}&=x +1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.002 |
|
| \begin{align*}
z^{\prime }+2 z x&=2 a \,x^{3} z^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.099 |
|
| \begin{align*}
z^{\prime }+z \cos \left (x \right )&=z^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.593 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.582 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
91.342 |
|
| \begin{align*}
x^{2}+y^{2}&=2 y y^{\prime } x \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.081 |
|
| \begin{align*}
y x -y^{2}-x^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.274 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.213 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.513 |
|
| \begin{align*}
\left (-x^{3}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.935 |
|
| \begin{align*}
y^{\prime } x +x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.384 |
|
| \begin{align*}
y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.243 |
|
| \begin{align*}
x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.542 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {y^{2}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.208 |
|
| \begin{align*}
2 \cos \left (x \right ) y^{\prime }&=\sin \left (x \right ) y-y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.033 |
|
| \begin{align*}
2 y y^{\prime } x +\left (x +1\right ) y^{2}&={\mathrm e}^{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.985 |
|
| \begin{align*}
x^{2} y+y^{2}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.398 |
|
| \begin{align*}
y^{\prime } x +y&=x^{2} \left ({\mathrm e}^{x}+1\right ) y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.074 |
|
| \begin{align*}
y^{\prime }+8 x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.405 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.042 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+y x -3 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.948 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.198 |
|
| \begin{align*}
2 y y^{\prime } x +3 x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.968 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.691 |
|
| \begin{align*}
y^{\prime }&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.395 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }&=1+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.601 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
y \left (5\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.671 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x y^{2}+x}{x^{2} y-y} \\
y \left (\sqrt {2}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.480 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-8 x&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.850 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.454 |
|
| \begin{align*}
y^{\prime }+y&=x y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.660 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=2 x^{{3}/{2}} \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.493 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +3 y^{3}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.214 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.434 |
|
| \begin{align*}
3 x^{3} y^{2} y^{\prime }-x^{2} y^{3}&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.652 |
|
| \begin{align*}
y^{\prime }-2 y-y^{2} {\mathrm e}^{3 x}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.543 |
|
| \begin{align*}
y^{\prime }+y x&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.692 |
|
| \begin{align*}
\left (x y^{2}+3 y^{2}\right ) y^{\prime }-2 x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.621 |
|
| \begin{align*}
y^{\prime } x&=\frac {1}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.071 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x +1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.873 |
|
| \begin{align*}
x v^{\prime }&=\frac {1-4 v^{2}}{3 v} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
46.612 |
|
| \begin{align*}
x^{\prime }-x^{3}&=x \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.285 |
|
| \begin{align*}
x +x y^{2}+{\mathrm e}^{x^{2}} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.440 |
|
| \begin{align*}
\frac {y^{\prime }}{y}+y \,{\mathrm e}^{\cos \left (x \right )} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.150 |
|
| \begin{align*}
x^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.565 |
|
| \begin{align*}
\sqrt {y}+\left (x +1\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.598 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x^{2}}}{y^{2}} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.787 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.745 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
105.859 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.663 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.850 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.283 |
|
| \begin{align*}
y^{\prime }&=x y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.553 |
|
| \begin{align*}
2 y+y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.836 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.052 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.582 |
|
| \begin{align*}
2 x y^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.909 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.173 |
|
| \begin{align*}
2 t x x^{\prime }+t^{2}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
85.622 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.682 |
|
| \begin{align*}
y \,{\mathrm e}^{-2 x}+y^{3}-{\mathrm e}^{-2 x} y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.862 |
|
| \begin{align*}
y x +y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.005 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.419 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.328 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}-y^{2}}{3 x y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.862 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.310 |
|
| \begin{align*}
y^{\prime }-y&={\mathrm e}^{2 x} y^{3} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.561 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y}{x}-y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.299 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x -2}&=5 \left (x -2\right ) \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.300 |
|
| \begin{align*}
x^{\prime }+t x^{3}+\frac {x}{t}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.781 |
|
| \begin{align*}
y^{\prime }+y&=\frac {{\mathrm e}^{x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.937 |
|
| \begin{align*}
r^{\prime }&=r^{2}+\frac {2 r}{t} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.864 |
|
| \begin{align*}
y^{\prime }+x y^{3}+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.908 |
|
| \begin{align*}
2 x y^{3}-\left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.319 |
|
| \begin{align*}
t^{3} y^{2}+\frac {t^{4} y^{\prime }}{y^{6}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
9.927 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=2 y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.037 |
|
| \begin{align*}
x^{2}+y^{2}+3 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.119 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.483 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
89.361 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-\frac {4 x}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.402 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (1\right ) &= -4 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.825 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.585 |
|
| \begin{align*}
\sqrt {y}+\left (x^{2}+4\right ) y^{\prime }&=0 \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
19.695 |
|
| \begin{align*}
y^{\prime }-\frac {2 y}{x}&=\frac {1}{y x} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.193 |
|
| \begin{align*}
y^{\prime }-4 y&=2 x y^{2} \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.819 |
|
| \begin{align*}
y^{\prime }&=2 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.662 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.111 |
|
| \begin{align*}
3 y^{\prime } x +y+x^{2} y^{4}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.822 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.030 |
|
| \begin{align*}
y^{\prime } x +3 y&=y^{2} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.322 |
|
| \begin{align*}
x^{3}+y^{3}&=3 y^{2} y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.382 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.516 |
|
| \begin{align*}
y^{\prime }+y&=y^{4} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.993 |
|
| \begin{align*}
2 y^{\prime }+y&=y^{3} \left (-1+x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.286 |
|
| \begin{align*}
y^{\prime }-2 \tan \left (x \right ) y&=y^{2} \tan \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
0.716 |
|
| \begin{align*}
y^{\prime }+\tan \left (x \right ) y&=y^{3} \sec \left (x \right )^{4} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.668 |
|
| \begin{align*}
y^{\prime }-\cot \left (x \right ) y&=y^{2} \sec \left (x \right )^{2} \\
y \left (\frac {\pi }{4}\right ) &= -1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.776 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.770 |
|
| \begin{align*}
x \left (1+y^{2}\right )-\left (x^{2}+1\right ) y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.261 |
|
| \begin{align*}
\frac {r \tan \left (\theta \right ) r^{\prime }}{a^{2}-r^{2}}&=1 \\
r \left (\frac {\pi }{4}\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.382 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.888 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.773 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.836 |
|
| \begin{align*}
y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.790 |
|
| \begin{align*}
y^{2}-x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.954 |
|
| \begin{align*}
x^{3}+y^{3}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.704 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.983 |
|
| \begin{align*}
y^{2}+y x -y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.685 |
|
| \begin{align*}
y \left (x -2 y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.802 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.068 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.490 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.432 |
|
| \begin{align*}
y^{\prime } x +y-x^{3} y^{6}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.536 |
|
| \begin{align*}
y y^{\prime }-x y^{2}+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.797 |
|
| \begin{align*}
2 x^{\prime }-\frac {x}{y}+x^{3} \cos \left (y \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.243 |
|
| \begin{align*}
2 x y^{5}-y+2 y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.000 |
|
| \begin{align*}
x y^{3}-y^{3}-{\mathrm e}^{x} x^{2}+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.938 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.437 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.615 |
|
| \begin{align*}
p^{\prime }&=p \left (1-p\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.177 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.131 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
6.395 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
5.221 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.186 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.903 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.013 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.855 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
64.929 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.852 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.456 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.899 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
32.727 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.239 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.783 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
36.928 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.448 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
96.718 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
138.284 |
|
| \begin{align*}
y^{\prime }&=y \left (y-3\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.409 |
|
| \begin{align*}
y^{\prime } x +y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
54.038 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.849 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.438 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.461 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.719 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
21.266 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.621 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.569 |
|
| \begin{align*}
p^{\prime }&=p-p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.503 |
|
| \begin{align*}
\left ({\mathrm e}^{x}+{\mathrm e}^{-x}\right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.602 |
|
| \begin{align*}
y^{\prime }&=y^{2} \sin \left (x^{2}\right ) \\
y \left (-2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.742 |
|
| \begin{align*}
y^{\prime }&=\frac {1+3 x}{2 y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.073 |
|
| \begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.093 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
22.959 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
62.693 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (\frac {1}{2}\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.351 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.552 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
13.780 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
13.570 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
5.757 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
11.702 |
|
| \begin{align*}
y^{\prime }&=\frac {\sin \left (\sqrt {x}\right )}{\sqrt {y}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
75.058 |
|
| \begin{align*}
\left (\sqrt {x}+x \right ) y^{\prime }&=\sqrt {y}+y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.398 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
83.786 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{\sqrt {x}}}{y} \\
y \left (1\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.419 |
|
| \begin{align*}
y^{\prime }&=\frac {x \arctan \left (x \right )}{y} \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.116 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.319 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
54.350 |
|
| \begin{align*}
m^{\prime }&=-\frac {k}{m^{2}} \\
m \left (0\right ) &= m_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
16.635 |
|
| \begin{align*}
y y^{\prime }-x&=2 y^{2} \\
y \left (1\right ) &= 5 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.879 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.577 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{\left (x^{3}+1\right ) y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.451 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.766 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.773 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.833 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.420 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.720 |
|
| \begin{align*}
{\mathrm e}^{x}-\left ({\mathrm e}^{x}+1\right ) y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.285 |
|
| \begin{align*}
\frac {y}{-1+x}+\frac {x y^{\prime }}{1+y}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.865 |
|
| \begin{align*}
\frac {1}{\sqrt {x}}+\frac {y^{\prime }}{\sqrt {y}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
119.333 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{\sqrt {x}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
115.690 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.813 |
|
| \begin{align*}
2 y^{\prime } x&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.808 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.579 |
|
| \begin{align*}
2 y^{\prime } x +\left (1+x^{2} y^{4}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.230 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.395 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{2 x}+\frac {x^{2}}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.935 |
|
| \begin{align*}
\phi ^{\prime }-\frac {\phi ^{2}}{2}-\phi \cot \left (\theta \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.889 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
64.326 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
99.434 |
|
| \begin{align*}
y y^{\prime }&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.731 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
38.795 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.339 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (x_{0} \right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.203 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.037 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.502 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
62.638 |
|
| \begin{align*}
x y^{2}-x^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.947 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.470 |
|
| \begin{align*}
\frac {y^{\prime }}{x^{2}+1}&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.684 |
|
| \begin{align*}
y^{2} y^{\prime }&=2+x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.295 |
|
| \begin{align*}
y^{\prime }&=y^{2} x^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.269 |
|
| \begin{align*}
y^{\prime } x +y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.569 |
|
| \begin{align*}
y^{2} y^{\prime } x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.581 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.487 |
|
| \begin{align*}
y^{\prime }+y x&=y^{4} x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
36.477 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
113.791 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.368 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.480 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
90.978 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.586 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.931 |
|
| \begin{align*}
y^{2} y^{\prime }&=x \\
y \left (-1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.725 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=6 y^{2} x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.227 |
|
| \begin{align*}
y^{\prime }+\frac {y}{3}&=\frac {\left (1-2 x \right ) y^{4}}{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.569 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
p \left (\operatorname {t0} \right ) &= \operatorname {p0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
78.215 |
|
| \begin{align*}
y^{2}+\frac {2}{x}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.444 |
|
| \begin{align*}
f^{\prime }&=\frac {1}{f} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.730 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
79.485 |
|
| \begin{align*}
y^{\prime }&=2 y \left (x \sqrt {y}-1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
13.480 |
|
| \begin{align*}
v v^{\prime }&=\frac {2 v^{2}}{r^{3}}+\frac {\lambda r}{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.266 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y^{2}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
37.444 |
|
| \begin{align*}
c y^{\prime }&=\frac {a x +b y^{2}}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.130 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
187.126 |
|
| \begin{align*}
y^{\prime }-x y^{2}-3 y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.293 |
|
| \begin{align*}
y^{\prime }+f \left (x \right ) y^{2}+g \left (x \right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.235 |
|
| \begin{align*}
y^{\prime }+2 a \,x^{3} y^{3}+2 y x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.021 |
|
| \begin{align*}
y^{\prime } x +x y^{2}-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.440 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.119 |
|
| \begin{align*}
y^{\prime } x -y \left (2 y \ln \left (x \right )-1\right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.271 |
|
| \begin{align*}
\left (x +1\right ) y^{\prime }+y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.125 |
|
| \begin{align*}
3 y^{\prime } x -3 x y^{4} \ln \left (x \right )-y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.247 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.456 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }-y \left (-x +y\right )&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.782 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+a x y^{2}+y x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.560 |
|
| \begin{align*}
\left (x^{2}-4\right ) y^{\prime }+\left (2+x \right ) y^{2}-4 y&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.546 |
|
| \begin{align*}
x^{3} y^{\prime }-y^{2}-x^{2} y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.612 |
|
| \begin{align*}
x^{2} \left (-1+x \right ) y^{\prime }-y^{2}-x \left (x -2\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.541 |
|
| \begin{align*}
\cos \left (x \right ) y^{\prime }-y^{4}-\sin \left (x \right ) y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.837 |
|
| \begin{align*}
y y^{\prime }+4 x \left (x +1\right )+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.085 |
|
| \begin{align*}
y y^{\prime }+a y^{2}-b \cos \left (x +c \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.298 |
|
| \begin{align*}
y y^{\prime }+x y^{2}-4 x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.855 |
|
| \begin{align*}
2 y y^{\prime }-x y^{2}-x^{3}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.408 |
|
| \begin{align*}
a y y^{\prime }+b y^{2}+f \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.892 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.796 |
|
| \begin{align*}
y y^{\prime } x -y^{2}+a \,x^{3} \cos \left (x \right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.825 |
|
| \begin{align*}
2 y y^{\prime } x -y^{2}+a x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.320 |
|
| \begin{align*}
2 y y^{\prime } x -y^{2}+a \,x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.900 |
|
| \begin{align*}
2 y y^{\prime } x +2 y^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.955 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}-2 x^{3}-x^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.109 |
|
| \begin{align*}
2 x^{2} y y^{\prime }-y^{2}-x^{2} {\mathrm e}^{x -\frac {1}{x}}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.660 |
|
| \begin{align*}
2 x^{3}+y y^{\prime }+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.237 |
|
| \begin{align*}
y y^{\prime } \sin \left (x \right )^{2}+y^{2} \cos \left (x \right ) \sin \left (x \right )-1&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.569 |
|
| \begin{align*}
f \left (x \right ) y y^{\prime }+g \left (x \right ) y^{2}+h \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.541 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.931 |
|
| \begin{align*}
6 y^{2} y^{\prime } x +x +2 y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.921 |
|
| \begin{align*}
x y^{3} y^{\prime }+y^{4}-x \sin \left (x \right )&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.128 |
|
| \begin{align*}
x \left (y^{\prime }+\sqrt {1+{y^{\prime }}^{2}}\right )-y&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.217 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1+\ln \left (x \left (x +1\right )\right ) y x^{4}-\ln \left (x \left (x +1\right )\right ) x^{3}\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
12.316 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (1-x +y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-1+x \right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.407 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}+y \ln \left (x \right ) x^{2}+x^{3} y-x \ln \left (x \right )-x^{2}\right )}{\left (-\ln \left (\frac {1}{x}\right )+{\mathrm e}^{x}\right ) x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.239 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-{\mathrm e}^{x}+\ln \left (2 x \right ) x^{2} y-\ln \left (2 x \right ) x \right ) {\mathrm e}^{-x}}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.027 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tan \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tan \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.874 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right ) x y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.742 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (x \right )-x \ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right )+\ln \left (\frac {\left (-1+x \right ) \left (x +1\right )}{x}\right ) x^{2} y\right )}{x \ln \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.168 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\ln \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \ln \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
10.224 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\tanh \left (\frac {1}{x}\right )-\ln \left (\frac {x^{2}+1}{x}\right ) x +\ln \left (\frac {x^{2}+1}{x}\right ) x^{2} y\right )}{x \tanh \left (\frac {1}{x}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
13.019 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\tanh \left (x \right )+\ln \left (2 x \right ) x -\ln \left (2 x \right ) x^{2} y\right )}{x \tanh \left (x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.520 |
|
| \begin{align*}
y^{\prime }&=-\frac {y \left (\ln \left (-1+x \right )+\coth \left (x +1\right ) x -\coth \left (x +1\right ) x^{2} y\right )}{x \ln \left (-1+x \right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
9.928 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-\cosh \left (\frac {1}{x +1}\right ) x +\cosh \left (\frac {1}{x +1}\right )-x +x^{2} y-x^{2}+x^{3} y\right )}{x \left (-1+x \right ) \cosh \left (\frac {1}{x +1}\right )} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
16.776 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-\cosh \left (\frac {x +1}{-1+x}\right ) x +\cosh \left (\frac {x +1}{-1+x}\right ) x^{2} y-\cosh \left (\frac {x +1}{-1+x}\right ) x^{2}+\cosh \left (\frac {x +1}{-1+x}\right ) x^{3} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
13.033 |
|
| \begin{align*}
y^{\prime }&=\frac {y \left (-1-x \,{\mathrm e}^{\frac {x +1}{-1+x}}+x^{2} {\mathrm e}^{\frac {x +1}{-1+x}} y-x^{2} {\mathrm e}^{\frac {x +1}{-1+x}}+x^{3} {\mathrm e}^{\frac {x +1}{-1+x}} y\right )}{x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
12.237 |
|
| \begin{align*}
g \left (x \right ) y^{\prime }&=f_{1} \left (x \right ) y+f_{n} \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.765 |
|
| \begin{align*}
\left (x +1\right ) y^{2}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.592 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.445 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
102.319 |
|
| \begin{align*}
y^{3}+x^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.016 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 \left (x +1\right ) y&=y^{{5}/{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
19.880 |
|
| \begin{align*}
y y^{\prime }+x y^{2}&=x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.038 |
|
| \begin{align*}
4 y^{\prime } x +3 y+{\mathrm e}^{x} x^{4} y^{5}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.369 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.814 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.070 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.023 |
|
| \begin{align*}
y^{\prime } x +y+{\mathrm e}^{x} x^{4} y^{4}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.071 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.778 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.345 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.650 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.318 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.187 |
|
| \begin{align*}
x^{\prime }&=x \left (1-\frac {x}{4}\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.420 |
|
| \begin{align*}
x^{\prime }&=\sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
8.802 |
|
| \begin{align*}
y^{\prime }+y+\frac {1}{y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.917 |
|
| \begin{align*}
\left (1+t \right ) x^{\prime }+x^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.742 |
|
| \begin{align*}
x^{\prime }&=2 t x^{2} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.622 |
|
| \begin{align*}
x^{\prime }&=x \left (4+x\right ) \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.259 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t y^{2}}{t^{2}+1} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
10.776 |
|
| \begin{align*}
x^{\prime }&=\frac {4 t^{2}+3 x^{2}}{2 t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.251 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 t y}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.909 |
|
| \begin{align*}
y^{\prime }&=-y^{2} {\mathrm e}^{-t^{2}} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.053 |
|
| \begin{align*}
x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
95.923 |
|
| \begin{align*}
x^{\prime }&=x \left (1+{\mathrm e}^{t} x\right ) \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.207 |
|
| \begin{align*}
x^{\prime }&=-\frac {x}{t}+\frac {1}{t x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
56.816 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.793 |
|
| \begin{align*}
x^{\prime }&=a x+b x^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
45.569 |
|
| \begin{align*}
w^{\prime }&=t w+t^{3} w^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.484 |
|
| \begin{align*}
x^{2}-t^{2} x^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.852 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.582 |
|
| \begin{align*}
y^{\prime } x +y&=x^{3} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.462 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x -2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
19.344 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
110.421 |
|
| \begin{align*}
4 x +3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.808 |
|
| \begin{align*}
y^{2}+2 y x -x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.141 |
|
| \begin{align*}
\left (x +4\right ) \left (1+y^{2}\right )+y \left (x^{2}+3 x +2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.542 |
|
| \begin{align*}
\left (3 x +8\right ) \left (4+y^{2}\right )-4 y \left (x^{2}+5 x +6\right ) y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.362 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\
y \left (2\right ) &= 6 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.322 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.299 |
|
| \begin{align*}
y^{\prime } x +y&=-2 x^{6} y^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.335 |
|
| \begin{align*}
y^{\prime }+\left (4 y-\frac {8}{y^{3}}\right ) x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.701 |
|
| \begin{align*}
x^{\prime }+\frac {\left (1+t \right ) x}{2 t}&=\frac {1+t}{t x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.670 |
|
| \begin{align*}
y^{\prime }+\frac {y}{2 x}&=\frac {x}{y^{3}} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.351 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
71.112 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.879 |
|
| \begin{align*}
8+2 y^{2}+\left (-x^{2}+1\right ) y y^{\prime }&=0 \\
y \left (3\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
13.393 |
|
| \begin{align*}
y^{2} {\mathrm e}^{2 x}-2 x +y \,{\mathrm e}^{2 x} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.333 |
|
| \begin{align*}
4 y y^{\prime } x&=1+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.868 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=\frac {y^{3}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
209.023 |
|
| \begin{align*}
x^{\prime }&=x \left (2-x\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.645 |
|
| \begin{align*}
x^{\prime }&=-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.303 |
|
| \begin{align*}
y^{\prime }&=y^{2} {\mathrm e}^{-t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.484 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
137.207 |
|
| \begin{align*}
x^{\prime }&=-x \left (k^{2}+x^{2}\right ) \\
x \left (0\right ) &= x_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✗ |
179.049 |
|
| \begin{align*}
V^{\prime }\left (x \right )+2 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.788 |
|
| \begin{align*}
x^{\prime }&=k x-x^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.262 |
|
| \begin{align*}
y&=y^{\prime } x +\frac {1}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
70.035 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x +1}+y^{2}&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.900 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.533 |
|
| \begin{align*}
x^{\prime }&=\frac {x}{t}+\frac {x^{2}}{t^{3}} \\
x \left (2\right ) &= 4 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.892 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}+x^{3} y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.060 |
|
| \begin{align*}
y \left (x -y\right )-x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.479 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.256 |
|
| \begin{align*}
3 y^{2} y^{\prime } x +y^{3}-2 x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.731 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.308 |
|
| \begin{align*}
y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.793 |
|
| \begin{align*}
x -x y^{2}+\left (y-x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.424 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{3}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
73.218 |
|
| \begin{align*}
y^{\prime }+y x&=x^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.586 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x +a x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.382 |
|
| \begin{align*}
3 y^{2} y^{\prime }-a y^{3}-x -1&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.726 |
|
| \begin{align*}
y^{\prime } x&=\left (y \ln \left (x \right )-2\right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.779 |
|
| \begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.864 |
|
| \begin{align*}
\frac {1}{x^{2}}+\frac {3 y^{2}}{x^{4}}&=\frac {2 y y^{\prime }}{x^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.213 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.550 |
|
| \begin{align*}
\frac {x^{2} y^{\prime }}{\left (x -y\right )^{2}}-\frac {y^{2}}{\left (x -y\right )^{2}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.960 |
|
| \begin{align*}
y^{\prime } x -y^{2} \ln \left (x \right )+y&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.241 |
|
| \begin{align*}
y^{\prime }+\frac {1}{2 y}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.992 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
50.833 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.217 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
43.132 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.157 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.406 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
44.456 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.103 |
|
| \begin{align*}
y^{\prime }&=-\frac {y}{x}+y^{{1}/{4}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
81.784 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.944 |
|
| \begin{align*}
y^{\prime }&=y^{2}-2 y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
7.300 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.495 |
|
| \begin{align*}
2 y y^{\prime } x +y^{2}&=-1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.396 |
|
| \begin{align*}
x -y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.115 |
|
| \begin{align*}
x y \left (1-y\right )-2 y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
20.173 |
|
| \begin{align*}
x \left (1-y^{3}\right )-3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.237 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.962 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
4.707 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.181 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.081 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.259 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.289 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.974 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.796 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.272 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x^{2}}{2 y} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.719 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
22.809 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.541 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
18.392 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
18.353 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
308.962 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
233.841 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
277.006 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
94.354 |
|
| \begin{align*}
y^{\prime }&=3 x y^{{1}/{3}} \\
y \left (-1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
269.750 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.503 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.694 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
55.782 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y+t^{2} y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.250 |
|
| \begin{align*}
y^{\prime }&=t y^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
66.010 |
|
| \begin{align*}
y^{\prime }&=y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.431 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.233 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.238 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
47.869 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y-t^{2} y} \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.309 |
|
| \begin{align*}
y^{\prime }&=t y^{2}+2 y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.718 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}}{x+t^{3} x} \\
x \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.394 |
|
| \begin{align*}
y^{\prime }&=\frac {1-y^{2}}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.199 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.389 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+5}{y} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.942 |
|
| \begin{align*}
y^{\prime }&=4 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
10.967 |
|
| \begin{align*}
y^{\prime }&=2 y \left (1-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.398 |
|
| \begin{align*}
y^{\prime }&=3 y \left (1-y\right ) \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
6.690 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
6.677 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.919 |
|
| \begin{align*}
y^{\prime }&=t y+t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.459 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
12.938 |
|
| \begin{align*}
y^{\prime }&=-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.090 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.531 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
9.046 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
8.722 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✓ |
8.302 |
|
| \begin{align*}
y^{\prime }&=3 y \left (y-2\right ) \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
7.473 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.948 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.882 |
|
| \begin{align*}
y^{\prime }&=2 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.138 |
|
| \begin{align*}
y^{\prime }&=t^{2} y^{3}+y^{3} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.940 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2}+3 t^{2} y^{2} \\
y \left (1\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.271 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{y+y t^{3}} \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.968 |
|
| \begin{align*}
y y^{\prime }&=2 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.375 |
|
| \begin{align*}
y^{3}-25 y+y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.881 |
|
| \begin{align*}
y^{\prime }&=2 \sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.417 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.261 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
53.077 |
|
| \begin{align*}
y y^{\prime } x&=y^{2}+9 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.997 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
55.201 |
|
| \begin{align*}
y y^{\prime }&=x y^{2}+x \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.996 |
|
| \begin{align*}
y y^{\prime }&=x y^{2}-9 x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.318 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
8.908 |
|
| \begin{align*}
y^{\prime }&=3 y^{2}-\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.726 |
|
| \begin{align*}
y^{\prime }&=3 x y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.330 |
|
| \begin{align*}
y^{\prime }&=200 y-2 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.872 |
|
| \begin{align*}
y y^{\prime }&=\sin \left (x \right ) \\
y \left (0\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.276 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.277 |
|
| \begin{align*}
y^{\prime } x&=y^{2}-y \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
21.845 |
|
| \begin{align*}
y^{\prime }&=\frac {-1+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
60.673 |
|
| \begin{align*}
y^{\prime }+4 y&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
7.842 |
|
| \begin{align*}
x^{2} y^{\prime }-y x&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.062 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.320 |
|
| \begin{align*}
y^{\prime }+3 y&=3 y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.658 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.461 |
|
| \begin{align*}
y^{\prime }+3 \cot \left (x \right ) y&=6 \cos \left (x \right ) y^{{2}/{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.382 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=\frac {1}{y} \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.095 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
85.847 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x}&=4 \sqrt {y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
118.115 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=x^{2} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.158 |
|
| \begin{align*}
y^{\prime }+3 y&=\frac {28 \,{\mathrm e}^{2 x}}{y^{3}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.547 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y}-\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.912 |
|
| \begin{align*}
2 x y^{3}+4 x^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.211 |
|
| \begin{align*}
2-2 x +3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.010 |
|
| \begin{align*}
1+3 y^{2} x^{2}+\left (2 x^{3} y+6 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.584 |
|
| \begin{align*}
1+y^{4}+x y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.277 |
|
| \begin{align*}
y^{\prime } x&=2 y^{2}-6 y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
54.367 |
|
| \begin{align*}
4 y^{2}-y^{2} x^{2}+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.278 |
|
| \begin{align*}
x y^{2}-6+x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.381 |
|
| \begin{align*}
x^{3}+y^{3}+y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
116.822 |
|
| \begin{align*}
1+2 x y^{2}+\left (2 x^{2} y+2 y\right ) y^{\prime }&=0 \\
\end{align*} |
[_exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.102 |
|
| \begin{align*}
3 x y^{3}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.212 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y}{x +1}-y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.716 |
|
| \begin{align*}
y y^{\prime } x&=2 x^{2}+2 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.973 |
|
| \begin{align*}
x y^{3} y^{\prime }&=y^{4}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
65.465 |
|
| \begin{align*}
y^{\prime }&=4 y-\frac {16 \,{\mathrm e}^{4 x}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.892 |
|
| \begin{align*}
y y^{\prime }-x y^{2}&=6 x \,{\mathrm e}^{4 x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.924 |
|
| \begin{align*}
y^{2}-y^{2} \cos \left (x \right )+y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.964 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.446 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.217 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}+2 y x}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.984 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{5}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
56.445 |
|
| \begin{align*}
\frac {y^{\prime }}{t}&=\sqrt {y} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.031 |
|
| \begin{align*}
y^{\prime }&=6 y^{{2}/{3}} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.306 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.531 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.723 |
|
| \begin{align*}
y^{\prime }&=-\frac {t}{y} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.402 |
|
| \begin{align*}
y^{\prime }&=-y^{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.973 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.249 |
|
| \begin{align*}
\frac {1}{2 \sqrt {t}}+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.885 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {y}}{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.671 |
|
| \begin{align*}
y^{\prime }&=\frac {1+y^{2}}{y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.575 |
|
| \begin{align*}
y^{\prime }&=\frac {5^{-t}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.085 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.299 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.813 |
|
| \begin{align*}
y^{\prime }&=y^{3}+y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.993 |
|
| \begin{align*}
y^{\prime }&=\frac {\sqrt {t}}{y} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.316 |
|
| \begin{align*}
y^{\prime }&=y^{2} \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.133 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y}\, \cos \left (t \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
4.987 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.411 |
|
| \begin{align*}
y^{\prime }&=16 y-8 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
1.988 |
|
| \begin{align*}
\frac {t}{\sqrt {t^{2}+y^{2}}}+\frac {y y^{\prime }}{\sqrt {t^{2}+y^{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.800 |
|
| \begin{align*}
-1+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.821 |
|
| \begin{align*}
3 t^{2}+3 y^{2}+6 t y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.523 |
|
| \begin{align*}
2 t y+y^{2}-t^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.142 |
|
| \begin{align*}
5 t y^{2}+y+\left (2 t^{3}-t \right ) y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.799 |
|
| \begin{align*}
-\frac {y}{2}+y^{\prime }&=\frac {t}{y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.473 |
|
| \begin{align*}
y+y^{\prime }&=t y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
2.520 |
|
| \begin{align*}
2 y^{\prime } t -y&=2 t y^{3} \cos \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.688 |
|
| \begin{align*}
-y+y^{\prime } t&=t y^{3} \sin \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.764 |
|
| \begin{align*}
-2 y+y^{\prime }&=\frac {\cos \left (t \right )}{\sqrt {y}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.759 |
|
| \begin{align*}
3 y+y^{\prime }&=\sqrt {y}\, \sin \left (t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.878 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.261 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.394 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.846 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=t^{2} y^{{3}/{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
114.626 |
|
| \begin{align*}
\frac {2}{t}+\frac {1}{y}+\frac {t y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.334 |
|
| \begin{align*}
\sqrt {t^{2}+1}+y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.809 |
|
| \begin{align*}
t^{3}+y^{3}-t y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.105 |
|
| \begin{align*}
y^{\prime }+2 y&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.421 |
|
| \begin{align*}
-2 y+y^{\prime }&=t^{2} \sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
2.424 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-t^{2}}{2 t y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.127 |
|
| \begin{align*}
y^{3}-t^{3}-t y^{2} y^{\prime }&=0 \\
y \left (1\right ) &= 3 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.054 |
|
| \begin{align*}
y^{\prime }+\cot \left (x \right ) y&=y^{4} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✗ |
82.036 |
|
| \begin{align*}
y^{\prime }&=\frac {-t^{2}+y^{2}}{t y} \\
y \left (4\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.207 |
|
| \begin{align*}
y^{\prime }&=\frac {2 t^{5}}{5 y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.694 |
|
| \begin{align*}
y^{\prime }-\frac {y}{t}&=\frac {y^{2}}{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.212 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{5 t}}{y^{4}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
2.533 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}+t^{2}}{r t} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.678 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.372 |
|
| \begin{align*}
y+y^{\prime }&=\frac {{\mathrm e}^{t}}{y^{2}} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.016 |
|
| \begin{align*}
y-y^{\prime } t&=2 y^{2} \ln \left (t \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.059 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
11.075 |
|
| \begin{align*}
y^{\prime }&=\frac {t}{y^{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.066 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.716 |
|
| \begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
3.764 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
2.791 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.643 |
|
| \begin{align*}
4 y^{6}+x^{3}&=6 x y^{5} y^{\prime } \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.434 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.487 |
|
| \begin{align*}
3 y^{2} y^{\prime } x -2 y^{3}&=x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.755 |
|
| \begin{align*}
2 \ln \left (x \right ) y^{\prime }+\frac {y}{x}&=\frac {\cos \left (x \right )}{y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.047 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \sin \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.553 |
|
| \begin{align*}
y^{\prime }-\cos \left (x \right ) y&=y^{2} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.585 |
|
| \begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.419 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.738 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.367 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.447 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.314 |
|
| \begin{align*}
y y^{\prime } x -y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.891 |
|
| \begin{align*}
y^{2} y^{\prime } x -y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.323 |
|
| \begin{align*}
x^{2}+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.283 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.918 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.112 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.424 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.888 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{4}}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.641 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2} \left (x^{3}+1\right )}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
3.239 |
|
| \begin{align*}
y^{\prime }+y^{3} \sin \left (x \right )&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.003 |
|
| \begin{align*}
y y^{\prime }&=\left (x y^{2}+x \right ) {\mathrm e}^{x^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.938 |
|
| \begin{align*}
y^{\prime }&=x \left (y-y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.183 |
|
| \begin{align*}
y^{\prime }&=\left (1-12 x \right ) y^{2} \\
y \left (0\right ) &= -{\frac {1}{8}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.315 |
|
| \begin{align*}
y^{\prime }&=\frac {3-2 x}{y} \\
y \left (1\right ) &= -6 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.964 |
|
| \begin{align*}
x +y y^{\prime } {\mathrm e}^{-x}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.635 |
|
| \begin{align*}
r^{\prime }&=\frac {r^{2}}{\theta } \\
r \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.605 |
|
| \begin{align*}
y^{\prime }&=\frac {3 x}{y+x^{2} y} \\
y \left (0\right ) &= -7 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.020 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2}+4 x^{3} y^{2} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.019 |
|
| \begin{align*}
y^{\prime }&=\frac {x \left (x^{2}+1\right ) y^{5}}{6} \\
y \left (0\right ) &= -2^{{1}/{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
4.281 |
|
| \begin{align*}
2 y y^{\prime }&=\frac {x}{\sqrt {x^{2}-4}} \\
y \left (3\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.647 |
|
| \begin{align*}
\sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.550 |
|
| \begin{align*}
y^{\prime }&=2 y^{2}+x y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.772 |
|
| \begin{align*}
y^{\prime }&=\frac {t \left (4-y\right ) y}{3} \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
7.724 |
|
| \begin{align*}
y^{\prime }&=\frac {t y \left (4-y\right )}{1+t} \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✓ |
10.547 |
|
| \begin{align*}
y^{\prime }&=y^{{1}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
62.139 |
|
| \begin{align*}
y^{\prime }&=-\frac {4 t}{y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
14.217 |
|
| \begin{align*}
y^{\prime }&=2 t y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.247 |
|
| \begin{align*}
y^{3}+y^{\prime }&=0 \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.211 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}}{\left (t^{3}+1\right ) y} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
4.849 |
|
| \begin{align*}
y^{\prime }&=t \left (3-y\right ) y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.467 |
|
| \begin{align*}
y^{\prime }&=y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.476 |
|
| \begin{align*}
y^{\prime }&=-y \left (3-t y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.399 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.694 |
|
| \begin{align*}
y y^{\prime }&=x +1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
5.955 |
|
| \begin{align*}
x \left (-1+x \right ) y^{\prime }&=y \left (1+y\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.840 |
|
| \begin{align*}
y y^{\prime } x&=x^{2}+y^{2} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.691 |
|
| \begin{align*}
y^{\prime } t +y&=t^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.706 |
|
| \begin{align*}
y^{\prime }&=y \left (t y^{3}-1\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.865 |
|
| \begin{align*}
y^{\prime }+\frac {3 y}{t}&=t^{2} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
4.900 |
|
| \begin{align*}
t^{2} y^{\prime }+2 t y-y^{3}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.437 |
|
| \begin{align*}
3 y^{\prime } t +9 y&=2 t y^{{5}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.817 |
|
| \begin{align*}
y^{\prime }&=y+\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.259 |
|
| \begin{align*}
y^{\prime }&=r y-k^{2} y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.635 |
|
| \begin{align*}
y^{\prime }&=a y+b y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.718 |
|
| \begin{align*}
y^{\prime }-4 y^{2} {\mathrm e}^{x}&=y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
3.835 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}-\frac {\sin \left (2 x \right )}{2}}{\left (-x^{2}+1\right ) y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.655 |
|
| \begin{align*}
2 y y^{\prime } x +\ln \left (x \right )&=-1-y^{2} \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.801 |
|
| \begin{align*}
4 y y^{\prime } x&=8 x^{2}+5 y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.412 |
|
| \begin{align*}
y^{\prime }+y-y^{{1}/{4}}&=0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
10.108 |
|
| \begin{align*}
y^{\prime } x -4 y&=\sqrt {y}\, x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.708 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.239 |
|
| \begin{align*}
y^{\prime }-\frac {x y}{2 x^{2}-2}-\frac {x}{2 y}&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
5.178 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.674 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.306 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.561 |
|
| \begin{align*}
y y^{\prime }&={\mathrm e}^{2 x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
6.351 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}+y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.731 |
|
| \begin{align*}
x^{5} y^{\prime }+y^{5}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.931 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.810 |
|
| \begin{align*}
x^{2} y^{\prime }-3 y x -2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.293 |
|
| \begin{align*}
x^{2} y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.986 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.124 |
|
| \begin{align*}
y^{\prime }&=\frac {1-x y^{2}}{2 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.840 |
|
| \begin{align*}
y^{\prime }&=\frac {2+3 x y^{2}}{4 x^{2} y} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.102 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.006 |
|
| \begin{align*}
\frac {x}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}+\frac {y y^{\prime }}{\left (x^{2}+y^{2}\right )^{{3}/{2}}}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.410 |
|
| \begin{align*}
x +3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.878 |
|
| \begin{align*}
x^{3}+x y^{3}+3 y^{2} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.405 |
|
| \begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.348 |
|
| \begin{align*}
2 x y^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.475 |
|
| \begin{align*}
y^{\prime } x +y&=x^{4} y^{3} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.681 |
|
| \begin{align*}
y^{2} y^{\prime } x +y^{3}&=\cos \left (x \right ) x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.921 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.134 |
|
| \begin{align*}
y^{\prime } x +y&=x^{2} y^{\prime }+y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.702 |
|
| \begin{align*}
x^{2} y^{4}+x^{6}-x^{3} y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
110.931 |
|
| \begin{align*}
x y^{2}+y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.220 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.713 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.168 |
|
| \begin{align*}
x^{\prime }&=2 \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
6.353 |
|
| \begin{align*}
x^{\prime }+2 t x+t x^{4}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.803 |
|
| \begin{align*}
2 x^{2} y+y^{3}-x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
78.564 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {\sin \left (x \right )}{y^{3}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.428 |
|
| \begin{align*}
\left (T \ln \left (t \right )-1\right ) T&=t T^{\prime } \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.931 |
|
| \begin{align*}
y-\cos \left (x \right ) y^{\prime }&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.930 |
|
| \begin{align*}
1+v^{2}+\left (u^{2}+1\right ) v v^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.296 |
|
| \begin{align*}
y^{\prime }+\sin \left (x \right ) y&=\sin \left (x \right ) y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.645 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-y x&=a x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.223 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.248 |
|
| \begin{align*}
3 y^{2} y^{\prime }+y^{3}&=-1+x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.376 |
|
| \begin{align*}
y^{\prime }-\tan \left (x \right ) y&=y^{4} \sec \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.284 |
|
| \begin{align*}
5 y y^{\prime } x -x^{2}-y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.305 |
|
| \begin{align*}
-y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.715 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.438 |
|
| \begin{align*}
{\mathrm e}^{x} x^{4}-2 m x y^{2}+2 m \,x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.151 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.520 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.568 |
|
| \begin{align*}
x^{2}+y^{2}-x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.070 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=y^{6} x^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.386 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=3 x^{2} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
104.536 |
|
| \begin{align*}
y^{\prime }+\frac {x y}{-x^{2}+1}&=x \sqrt {y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.222 |
|
| \begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=a \,x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.158 |
|
| \begin{align*}
3 y^{\prime }+\frac {2 y}{x +1}&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.963 |
|
| \begin{align*}
y^{\prime } x +\frac {y^{2}}{x}&=y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.177 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.545 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.493 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{3}-y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.008 |
|
| \begin{align*}
y y^{\prime }&=a x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.895 |
|
| \begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.346 |
|
| \begin{align*}
x y \left (-y^{\prime } x +y\right )&=x +y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.375 |
|
| \begin{align*}
\sqrt {x}\, y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.707 |
|
| \begin{align*}
\left (y x +1\right ) y-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.431 |
|
| \begin{align*}
\sin \left (x \right ) y^{\prime }-\cos \left (x \right ) y+y^{2}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
7.890 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
16.447 |
|
| \begin{align*}
x y^{2}+x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.486 |
|
| \begin{align*}
-y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.471 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.718 |
|
| \begin{align*}
x^{2} y^{\prime }+y \left (x +y\right )&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
32.464 |
|
| \begin{align*}
2 y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
69.573 |
|
| \begin{align*}
x^{2}+3 y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.277 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.763 |
|
| \begin{align*}
2 y^{\prime }-y \sec \left (x \right )&=y^{3} \tan \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
18.213 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.872 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.924 |
|
| \begin{align*}
y^{\prime }&=\frac {1+x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
8.245 |
|
| \begin{align*}
y y^{\prime }+b y^{2}&=a \cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.173 |
|
| \begin{align*}
y \left ({\mathrm e}^{x}+2 y x \right )-{\mathrm e}^{x} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.096 |
|
| \begin{align*}
y&=y^{\prime } x +x \sqrt {1+{y^{\prime }}^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.642 |
|
| \begin{align*}
y^{2} x^{2}-3 y y^{\prime } x&=2 y^{2}+x^{3} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
11.435 |
|
| \begin{align*}
-y^{\prime } x +y&=a \left (y^{\prime }+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.872 |
|
| \begin{align*}
1+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.493 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.277 |
|
| \begin{align*}
x y \left (-y^{\prime } x +y\right )&=x +y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.615 |
|
| \begin{align*}
y^{\prime }&=\frac {{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
8.477 |
|
| \begin{align*}
y^{\prime }&=y^{2} \left (t^{2}+1\right ) \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.046 |
|
| \begin{align*}
y^{\prime } x&=y \left (1-2 y\right ) \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
12.066 |
|
| \begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.494 |
|
| \begin{align*}
y^{\prime }+2 y x&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.145 |
|
| \begin{align*}
y^{\prime }+2 y x&=y^{2} {\mathrm e}^{x^{2}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.970 |
|
| \begin{align*}
y^{\prime }&=\frac {y x +y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.263 |
|
| \begin{align*}
y^{\prime }&=k y-c y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
99.717 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.352 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {1}{4}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.687 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= {\frac {3}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.608 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.283 |
|
| \begin{align*}
y^{\prime }&=y-\mu y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.981 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.899 |
|
| \begin{align*}
\left (y x +1\right ) y&=y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.418 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{{1}/{3}}}{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
56.574 |
|
| \begin{align*}
x^{\prime }&=x^{2} \\
x \left (t_{0} \right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.155 |
|
| \begin{align*}
x^{\prime }&=x^{{1}/{4}} \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
61.595 |
|
| \begin{align*}
x^{\prime }&=x^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.941 |
|
| \begin{align*}
x^{\prime }&=x^{3}-x \\
x \left (0\right ) &= a \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.923 |
|
| \begin{align*}
x^{\prime }&=x^{2}+x \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.819 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} x^{4} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.269 |
|
| \begin{align*}
x^{\prime }&=-t x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.728 |
|
| \begin{align*}
x^{\prime }&=\frac {t}{x} \\
x \left (\sqrt {2}\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.991 |
|
| \begin{align*}
x^{\prime }&=-\frac {t}{4 x^{3}} \\
x \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.412 |
|
| \begin{align*}
x^{\prime }&=-t^{2} x^{2} \\
x \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
20.361 |
|
| \begin{align*}
x^{\prime }&=5 t \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
34.257 |
|
| \begin{align*}
x^{\prime }&=4 t^{3} \sqrt {x} \\
x \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
36.319 |
|
| \begin{align*}
x^{\prime }&=2 t \sqrt {x} \\
x \left (a \right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
70.529 |
|
| \begin{align*}
x^{\prime }&=-\left (1+p \right ) t^{p} x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.126 |
|
| \begin{align*}
x -2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.655 |
|
| \begin{align*}
x +y^{2}+B \left (x \right ) y y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.251 |
|
| \begin{align*}
x +y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.686 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.020 |
|
| \begin{align*}
x^{\prime }&=\frac {3 x^{2}-2 t^{2}}{t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.451 |
|
| \begin{align*}
x^{\prime }&=\frac {t^{2}+x^{2}}{2 t x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.246 |
|
| \begin{align*}
x^{\prime }-x&=t x^{2} \\
x \left (0\right ) &= a \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.184 |
|
| \begin{align*}
x^{\prime }+2 t x&=-4 t x^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
43.007 |
|
| \begin{align*}
x^{\prime }-t x&=x^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
6.656 |
|
| \begin{align*}
x^{\prime }&=\lambda x-x^{5} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.008 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
25.553 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.034 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (0\right ) &= a_{0} \\
\end{align*} |
[_separable] |
✓ |
✗ |
✓ |
✓ |
30.546 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.234 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y^{2} \sqrt {x^{2}+1}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
16.444 |
|
| \begin{align*}
x y^{2}-x +\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.868 |
|
| \begin{align*}
y^{\prime }&=x^{2} y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.922 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.365 |
|
| \begin{align*}
x^{2}-2 y^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
89.158 |
|
| \begin{align*}
y^{2}-x^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.217 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{3}-2 x^{3}}{x y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.548 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
136.889 |
|
| \begin{align*}
2 y y^{\prime } x&=y^{2}-x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.312 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
132.489 |
|
| \begin{align*}
x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
91.184 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.240 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
y \left (1\right ) &= -2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
30.359 |
|
| \begin{align*}
y-x y^{2}+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
9.404 |
|
| \begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
13.557 |
|
| \begin{align*}
\frac {y^{2}-y x}{x y^{2}}+\frac {x y^{\prime }}{y^{2}}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.062 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2} x^{2}+2 y}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.046 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.040 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.700 |
|
| \begin{align*}
y \left (6 y^{2}-x -1\right )+2 y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
14.017 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.388 |
|
| \begin{align*}
y^{\prime }&=\alpha \left (A -y\right ) y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
32.684 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.828 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{4 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
23.231 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.230 |
|
| \begin{align*}
3 x^{2}-2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
34.781 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.055 |
|
| \begin{align*}
x^{3}-y^{3}+y^{2} y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.997 |
|
| \begin{align*}
x y \left (y^{\prime } x +y\right )&=4 x^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.644 |
|
| \begin{align*}
y y^{\prime }+\tan \left (x \right ) y^{2}&=\cos \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.654 |
|
| \begin{align*}
-y+y^{\prime } x&=y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
33.459 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} x^{3} \sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
15.170 |
|
| \begin{align*}
x y^{2}&=-y^{\prime } x +y \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
25.766 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.452 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
9.495 |
|
| \begin{align*}
\sin \left (x \right )+y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.894 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
64.533 |
|
| \begin{align*}
x -y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
35.332 |
|
| \begin{align*}
y^{\prime }&=x^{3} y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.022 |
|
| \begin{align*}
{\mathrm e}^{x}-y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
10.570 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.737 |
|
| \begin{align*}
\sin \left (x \right )+y y^{\prime }&=0 \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.115 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{x}}{2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
7.302 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y^{4}+x^{4}}{x y^{3}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
141.427 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+2 y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
43.591 |
|
| \begin{align*}
y^{\prime }&=\frac {2 x +y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.629 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
31.945 |
|
| \begin{align*}
y^{\prime } x -y+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.382 |
|
| \begin{align*}
y^{\prime }&=\frac {-y+x y^{2}}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
10.407 |
|
| \begin{align*}
y+x^{3} y^{3}+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
26.194 |
|
| \begin{align*}
y+y^{2} x^{4}+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.135 |
|
| \begin{align*}
1-2 y y^{\prime } x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
15.252 |
|
| \begin{align*}
2 x y^{2}+\frac {x}{y^{2}}+4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.749 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.978 |
|
| \begin{align*}
y^{\prime }-\frac {3 y}{x}&=x^{4} y^{{1}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.338 |
|
| \begin{align*}
y^{\prime }+y&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.705 |
|
| \begin{align*}
y^{\prime }+y x&=6 x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
22.787 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=-x^{9} y^{5} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.693 |
|
| \begin{align*}
y^{\prime }&=y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
30.125 |
|
| \begin{align*}
y^{\prime }&=y^{p} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
34.739 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.753 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
30.326 |
|
| \begin{align*}
3 x \left (1+y^{2}\right )+y \left (x^{2}+2\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.282 |
|
| \begin{align*}
y^{\prime }&=\frac {x y^{2}+x}{4 y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
11.362 |
|
| \begin{align*}
y^{\prime }&=-\frac {3 x +x y^{2}}{x^{2} y+2 y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
16.328 |
|
| \begin{align*}
y^{\prime }&=\frac {4 y^{2}-x^{4}}{4 y x} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
30.244 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}+\frac {y^{2}}{x^{2}} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
24.777 |
|
| \begin{align*}
x^{2}-y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.459 |
|
| \begin{align*}
x^{3}+y^{3}-y^{2} y^{\prime } x&=0 \\
y \left (1\right ) &= 0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.914 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{2 y}+\frac {y}{2 x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
54.501 |
|
| \begin{align*}
2+3 x y^{2}-4 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.488 |
|
| \begin{align*}
3 x +4 y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
37.168 |
|
| \begin{align*}
2 y y^{\prime } x&=x^{2}-y^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.353 |
|
| \begin{align*}
y^{2}+2 x^{2}+y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.806 |
|
| \begin{align*}
3 x +2 y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
40.115 |
|
| \begin{align*}
y^{\prime }&=\frac {3 \cot \left (x \right ) y^{2}+\cos \left (x \right ) \sin \left (x \right )}{2 y} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
37.916 |
|
| \begin{align*}
y^{\prime }-y&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.290 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.685 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.856 |
|
| \begin{align*}
\left (x^{2}+1\right ) \left (y^{3}-1\right )&=x^{2} y^{2} y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
36.149 |
|
| \begin{align*}
s^{2} t s^{\prime }+t^{2}+4&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.075 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.460 |
|
| \begin{align*}
y^{\prime }&=\frac {2 y x -y^{4}}{3 x^{2}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.980 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.237 |
|
| \begin{align*}
x^{2}-y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
110.533 |
|
| \begin{align*}
3 x y^{2}+2+2 x^{2} y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.277 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.786 |
|
| \begin{align*}
y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✗ |
✓ |
11.054 |
|
| \begin{align*}
y^{2}+y y^{\prime } x&=\sin \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
27.604 |
|
| \begin{align*}
y^{\prime }&=\frac {x +y^{2}}{2 y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
11.365 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.105 |
|
| \begin{align*}
y y^{\prime }&=x^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
31.633 |
|
| \begin{align*}
y^{\prime } x&=\left (x +1\right ) y^{2} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.950 |
|
| \begin{align*}
x y \left (x^{2}+1\right ) y^{\prime }-y^{2}&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
43.408 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.223 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
47.518 |
|
| \begin{align*}
r r^{\prime }&=a \\
r \left (0\right ) &= b \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
16.842 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.092 |
|
| \begin{align*}
y y^{\prime }-y^{2}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.629 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.495 |
|
| \begin{align*}
y^{\prime }&=-\frac {x^{2}+y^{2}}{2 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.851 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
14.946 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
82.349 |
|
| \begin{align*}
x^{\prime }&=\frac {a x^{{5}/{6}}}{\left (-B t +b \right )^{{3}/{2}}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
116.288 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.259 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
13.013 |
|
| \begin{align*}
p^{\prime }&=a p-b p^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
46.953 |
|
| \begin{align*}
y^{\prime } x -\frac {y}{\ln \left (x \right )}&=x y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.073 |
|
| \begin{align*}
\left (1+y^{2}\right ) \cos \left (x \right )&=2 \left (1+\sin \left (x \right )^{2}\right ) y y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
24.191 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
63.941 |
|
| \begin{align*}
y^{\prime }+\frac {y}{\sin \left (x \right )}-y^{2}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.881 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=-\frac {1}{2 y} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.315 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=-2 x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
20.484 |
|
| \begin{align*}
y^{\prime }-2 y x&=4 x \sqrt {y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
29.796 |
|
| \begin{align*}
y^{\prime } x -\frac {y}{2 \ln \left (x \right )}&=y^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
22.154 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
67.572 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
58.340 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.436 |
|
| \begin{align*}
x^{2}+y^{2}+2 y y^{\prime } x&=0 \\
y \left (1\right ) &= -1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.201 |
|
| \begin{align*}
x^{4}+y^{4}-x y^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
154.262 |
|
| \begin{align*}
x^{2}-y^{2}+x +2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
13.486 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.777 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.433 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
50.933 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.820 |
|
| \begin{align*}
y y^{\prime }&=3 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
4.810 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x}-\frac {x}{y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.184 |
|
| \begin{align*}
y^{\prime }-\frac {y}{x}&=y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
57.195 |
|
| \begin{align*}
\left (x^{2}+1\right ) y y^{\prime }+4&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
14.895 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.325 |
|
| \begin{align*}
\left (x^{3}+1\right ) y^{\prime }+x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.115 |
|
| \begin{align*}
y^{2} \sec \left (x \right )^{2} y^{\prime }+x&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
45.514 |
|
| \begin{align*}
y y^{\prime } x +x^{6}-2 y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
44.818 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
116.934 |
|
| \begin{align*}
y^{3}+2 x y^{3}+1+3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.339 |
|
| \begin{align*}
y^{\prime }+p \left (x \right ) y&=q \left (x \right ) y^{n} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.349 |
|
| \begin{align*}
y^{\prime }-4 y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.832 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {x^{2}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
193.550 |
|
| \begin{align*}
y^{5} y^{\prime }+5 y^{6}&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
5.965 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{5} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
47.891 |
|
| \begin{align*}
y^{5} x^{2}+{\mathrm e}^{x^{3}} y^{\prime }&=0 \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
19.521 |
|
| \begin{align*}
y y^{\prime } x +2 x +\frac {y^{2}}{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
54.224 |
|
| \begin{align*}
x^{2} y^{\prime }-y^{2}&=2 y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.063 |
|
| \begin{align*}
3 y^{2}-2 x^{2}&=2 y y^{\prime } x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
142.880 |
|
| \begin{align*}
\left (1-x \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
17.092 |
|
| \begin{align*}
x y^{3}+{\mathrm e}^{x^{2}} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.708 |
|
| \begin{align*}
y^{\prime }&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
53.638 |
|
| \begin{align*}
x^{2}+y \left (-1+x \right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
18.656 |
|
| \begin{align*}
y y^{\prime } x -y^{2}&=1 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
44.732 |
|
| \begin{align*}
x y^{2}+{\mathrm e}^{x} y^{\prime }&=0 \\
y \left (\infty \right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
23.563 |
|
| \begin{align*}
v v^{\prime }&=g \\
v \left (x_{0} \right ) &= v_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✗ |
✓ |
✓ |
20.682 |
|
| \begin{align*}
2 y^{2}+4 x^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
83.444 |
|
| \begin{align*}
x^{2}+2 y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
76.336 |
|
| \begin{align*}
y y^{\prime } x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.096 |
|
| \begin{align*}
v \left (3 x +2 v\right )-x^{2} v^{\prime }&=0 \\
v \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.262 |
|
| \begin{align*}
1+y^{2}+\left (y+x^{2} y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
38.888 |
|
| \begin{align*}
1+y^{2}+x y^{2}+\left (x^{2} y+y+2 y x \right ) y^{\prime }&=0 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.306 |
|
| \begin{align*}
y \left (2 y x +1\right )-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
48.764 |
|
| \begin{align*}
x^{3} y^{3}+1+x^{4} y^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
63.323 |
|
| \begin{align*}
s \left (2+s^{2} t \right )+2 t s^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
75.481 |
|
| \begin{align*}
y \left (2-3 y x \right )-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
72.659 |
|
| \begin{align*}
y \left (3 x^{3}-x +y\right )+x^{2} \left (-x^{2}+1\right ) y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
12.511 |
|
| \begin{align*}
2 x^{5} y^{\prime }&=y \left (3 x^{4}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.691 |
|
| \begin{align*}
x^{2}+1+x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
40.014 |
|
| \begin{align*}
y^{\prime } x&=y^{2} x^{2}+2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
68.766 |
|
| \begin{align*}
y \left (x +3 y\right )+x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
111.454 |
|
| \begin{align*}
y^{\prime } x&=y \left (2 y x +1\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.009 |
|
| \begin{align*}
y \left (y^{2}-3 x^{2}\right )+x^{3} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
176.378 |
|
| \begin{align*}
y^{\prime }&=y-x y^{3} {\mathrm e}^{-2 x} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.741 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=y \left (3 x^{2}+y^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.843 |
|
| \begin{align*}
y^{\prime } x&=y-y^{3} \cos \left (x \right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.951 |
|
| \begin{align*}
-y+y^{\prime } x&=x^{k} y^{n} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
123.399 |
|
| \begin{align*}
2 y y^{\prime } x&=y^{2}-2 x^{3} \\
y \left (1\right ) &= 2 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.215 |
|
| \begin{align*}
y^{4}-2 y x +3 x^{2} y^{\prime }&=0 \\
y \left (2\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
46.575 |
|
| \begin{align*}
2 y^{3}-x^{3}+3 y^{2} y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
115.657 |
|
| \begin{align*}
x^{2}+6 y^{2}-4 y y^{\prime } x&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.893 |
|
| \begin{align*}
y^{\prime } x&=x^{3} y^{3}-2 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
118.165 |
|
| \begin{align*}
4 y+3 \left (2 x -1\right ) \left (y^{\prime }+y^{4}\right )&=0 \\
y \left (1\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.093 |
|
| \begin{align*}
y^{\prime }&=2 y \left (y-1\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.677 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.211 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.039 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
12.415 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
21.421 |
|
| \begin{align*}
y^{\prime }&=y^{2}-y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
21.819 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.701 |
|
| \begin{align*}
y^{\prime }&=y \left (y+t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.737 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
73.234 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.684 |
|
| \begin{align*}
y^{\prime }&=y \left (y+t \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
17.380 |
|
| \begin{align*}
y^{\prime }&=2 y \left (5-y\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.177 |
|
| \begin{align*}
\frac {y^{\prime }}{y}&=y-t \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
19.874 |
|
| \begin{align*}
{\mathrm e}^{t} y^{\prime }&=y^{3}-y \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
67.714 |
|
| \begin{align*}
y y^{\prime }&=t \\
y \left (2\right ) &= -1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
92.450 |
|
| \begin{align*}
1-y^{2}-t y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
121.653 |
|
| \begin{align*}
y^{3} y^{\prime }&=t \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
98.757 |
|
| \begin{align*}
y^{4} y^{\prime }&=t +2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.928 |
|
| \begin{align*}
y^{\prime }&=t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
68.645 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
127.409 |
|
| \begin{align*}
y^{\prime }&=4 y-y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.772 |
|
| \begin{align*}
y y^{\prime }&=1+y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.132 |
|
| \begin{align*}
t y y^{\prime }+t^{2}+1&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.466 |
|
| \begin{align*}
2 y y^{\prime }&={\mathrm e}^{t} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
26.736 |
|
| \begin{align*}
\left (1-t \right ) y^{\prime }&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
21.738 |
|
| \begin{align*}
-y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
20.774 |
|
| \begin{align*}
y^{\prime }&=4 t y^{2} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
86.935 |
|
| \begin{align*}
y^{\prime }&=\frac {3 y^{2}-t^{2}}{2 t y} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
176.750 |
|
| \begin{align*}
y^{\prime }&=\frac {t^{2}+y^{2}}{t y} \\
y \left ({\mathrm e}\right ) &= 2 \,{\mathrm e} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
106.819 |
|
| \begin{align*}
-y+y^{\prime }&=t y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
86.715 |
|
| \begin{align*}
y+y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
16.792 |
|
| \begin{align*}
t y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
72.893 |
|
| \begin{align*}
t y+y^{\prime }&=t^{3} y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
21.721 |
|
| \begin{align*}
\left (-t^{2}+1\right ) y^{\prime }-t y&=5 t y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
64.573 |
|
| \begin{align*}
\frac {y}{t}+y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
318.047 |
|
| \begin{align*}
y y^{\prime }+t y^{2}&=t \\
y \left (0\right ) &= -2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
27.944 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.030 |
|
| \begin{align*}
y+y^{\prime }&=t y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
42.455 |
|
| \begin{align*}
2 y y^{\prime }&=y^{2}+t -1 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.659 |
|
| \begin{align*}
y^{2}+2 t y y^{\prime }+3 t^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.467 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
27.444 |
|
| \begin{align*}
y^{\prime }&=y^{3}-y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
22.404 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (1\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
25.938 |
|
| \begin{align*}
y^{\prime }&=\sqrt {y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
30.874 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.823 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (t_{0} \right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
84.074 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
89.326 |
|
| \begin{align*}
y^{\prime }&=y^{2}+y \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
18.391 |
|
| \begin{align*}
y^{\prime }&=a y-b y^{n} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✗ |
42.691 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
17.798 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
22.974 |
|
| \begin{align*}
y^{\prime }&=-y^{2}+y \\
y \left (0\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
16.255 |
|
| \begin{align*}
y^{\prime }&=a y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
146.645 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.463 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= y_{0} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
49.542 |
|
| \begin{align*}
y^{\prime }&=t^{m} y^{n} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✗ |
✗ |
275.803 |
|
| \begin{align*}
y^{\prime }&=a \left (t \right ) y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
32.412 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}}{t^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
66.892 |
|
| \begin{align*}
y^{\prime }&=t y^{3} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
53.456 |
|
| \begin{align*}
y^{\prime }&=2 x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
83.838 |
|
| \begin{align*}
2 y^{\prime }&=y^{3} \cos \left (x \right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
46.549 |
|
| \begin{align*}
p^{\prime }&=p \left (1-p\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
23.412 |
|
| \begin{align*}
y^{\prime }&=-\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
90.290 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (0\right ) &= -{\frac {1}{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
19.171 |
|
| \begin{align*}
y^{\prime }&=y-y^{2} \\
y \left (-1\right ) &= 2 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.391 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (2\right ) &= {\frac {1}{3}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
70.939 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (-2\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
62.579 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
65.083 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
y \left (\frac {1}{2}\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
61.766 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
178.660 |
|
| \begin{align*}
y^{\prime }&=y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
39.030 |
|
| \begin{align*}
y^{\prime }&=y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
28.136 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (-2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
87.531 |
|
| \begin{align*}
y y^{\prime }&=3 x \\
y \left (2\right ) &= -4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
75.425 |
|
| \begin{align*}
y^{\prime }&=x \sqrt {y} \\
y \left (2\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
287.003 |
|
| \begin{align*}
y^{\prime }&=y \left (y-3\right ) \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
15.213 |
|
| \begin{align*}
y^{\prime } x +y&=\frac {1}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
147.900 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
81.240 |
|
| \begin{align*}
y y^{\prime }&=-x \\
y \left (0\right ) &= 4 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
91.059 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
14.224 |
|
| \begin{align*}
y^{\prime }&=\frac {1}{y} \\
y \left (-2\right ) &= -1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.052 |
|
| \begin{align*}
y^{\prime }&=y-y^{3} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
69.560 |
|
| \begin{align*}
y^{\prime }&=y^{2}-3 y \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
11.029 |
|
| \begin{align*}
y^{\prime }+2 x y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
77.273 |
|
| \begin{align*}
\sin \left (3 x \right )+2 y \cos \left (3 x \right )^{3} y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
54.319 |
|
| \begin{align*}
y^{\prime }&=-\frac {1}{2 y} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
9.894 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
88.428 |
|
| \begin{align*}
2 y y^{\prime } x -1-y^{2}&=0 \\
y \left (2\right ) &= 3 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
58.837 |
|
| \begin{align*}
\left (2 x^{2}+1\right ) y y^{\prime }&=2 x \left (1+y^{2}\right ) \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
62.770 |
|
| \begin{align*}
y^{3}+y^{\prime } \sqrt {-x^{2}+1}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
65.773 |
|
| \begin{align*}
x^{3}+y^{4} x +2 y^{3} y^{\prime }&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.569 |
|
| \begin{align*}
x^{\prime }-\frac {2 x}{y}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
143.725 |
|
| \begin{align*}
y y^{\prime }+\cot \left (x \right ) y^{2}&=\csc \left (x \right )^{2} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
38.376 |
|
| \begin{align*}
y^{\prime } x +y&=3 x^{3} y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
90.372 |
|
| \begin{align*}
\left (x -2\right ) y^{\prime }+y&=5 \left (x -2\right )^{2} \sqrt {y} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
89.842 |
|
| \begin{align*}
y^{\prime } x +y&=x y^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
29.425 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
y \left (1\right ) &= 1 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
97.516 |
|
| \begin{align*}
y^{\prime }&=\frac {6 x^{2}-7 y^{2}}{14 y x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
120.070 |
|
| \begin{align*}
y^{\prime }&=\frac {x^{3}+y^{3}}{y^{2} x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
216.221 |
|
| \begin{align*}
-y^{\prime } x +y&=a y^{2}+a y^{\prime } \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
63.974 |
|
| \begin{align*}
3 x \left (-x^{2}+1\right ) y^{2} y^{\prime }+\left (2 x^{2}-1\right ) y^{3}&=x^{2} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
92.255 |
|
| \begin{align*}
x^{2} y^{\prime }+y^{2}&=y x \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
55.598 |
|
| \begin{align*}
2 y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
62.670 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
90.771 |
|
| \begin{align*}
y y^{\prime } x&=2 y^{2}-3 x^{2} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
175.082 |
|
| \begin{align*}
x y^{2}+x^{2} y y^{\prime }&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
52.928 |
|
| \begin{align*}
y^{\prime }+y&=\epsilon y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
26.789 |
|
| \begin{align*}
y y^{\prime }&=-2 x^{3}+x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
28.441 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
98.447 |
|
| \begin{align*}
y^{\prime }&=3 y^{2} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
24.811 |
|
| \begin{align*}
x^{2}+y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
151.000 |
|
| \begin{align*}
y^{2} y^{\prime } x +y^{3}&=\frac {1}{x} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
110.057 |
|
| \begin{align*}
y&=y^{\prime } x +y^{2} \sin \left (x^{2}\right ) \\
\end{align*} |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
39.953 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
114.757 |
|
| \begin{align*}
y^{\prime }&=y+3 y^{{1}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
44.845 |
|
| \begin{align*}
y^{\prime }&=\frac {-1+x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
72.652 |
|
| \begin{align*}
y^{\prime }&=\frac {y}{x +1}-y^{2} \\
y \left (0\right ) &= 1 \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
61.977 |
|
| \begin{align*}
y y^{\prime } x +1+y^{2}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
81.502 |
|
| \begin{align*}
x -y^{2}+2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
53.894 |
|
| \begin{align*}
x y^{2} \left (y^{\prime } x +y\right )&=a^{2} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
113.055 |
|
| \begin{align*}
\ln \left (x \right )+y^{3}-3 y^{2} y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
67.476 |
|
| \begin{align*}
y^{\prime }&=y^{a} \\
y \left (0\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✗ |
✗ |
223.060 |
|
| \begin{align*}
3 y^{\prime } x -2 y&=\frac {x^{3}}{y^{2}} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
236.564 |
|
| \begin{align*}
8 y^{\prime } x -y&=-\frac {1}{y^{3} \sqrt {x +1}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
127.348 |
|
| \begin{align*}
x^{2} y^{\prime }+2 x^{3} y&=y^{2} \left (x^{3}+1\right ) \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
33.253 |
|
| \begin{align*}
2 \sin \left (x \right ) y^{\prime }+\cos \left (x \right ) y&=y^{3} \left (\cos \left (x \right ) x -\sin \left (x \right )\right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
49.824 |
|
| \begin{align*}
y^{\prime }+\frac {y \left (x +\frac {1}{2}\right )}{x^{2}+x +1}&=\frac {\left (-x^{2}+1\right ) y^{2}}{\left (x^{2}+x +1\right )^{{3}/{2}}} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.836 |
|
| \begin{align*}
3 y^{\prime }+\frac {y \left (a^{2}+x^{2}\right )}{x \left (-a^{2}+x^{2}\right )}&=\frac {x \left (-a^{2}+3 x^{2}\right )}{y^{2} \left (-a^{2}+x^{2}\right )} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
72.504 |
|
| \begin{align*}
\left (x^{2}+1\right ) y^{\prime }&=y^{2} x^{2}+y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
23.391 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x +1}&=-\frac {\left (x +1\right )^{3} y^{3}}{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
81.804 |
|
| \begin{align*}
x^{2}+y^{2}+1-2 y y^{\prime } x&=0 \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
36.506 |
|
| \begin{align*}
y \left (x^{2}+y^{2}\right )+x^{2} y^{\prime }-y x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
70.178 |
|
| \begin{align*}
x +y^{2}-2 y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.947 |
|
| \begin{align*}
x^{4} \ln \left (x \right )-2 x y^{3}+3 x^{2} y^{2} y^{\prime }&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.020 |
|
| \begin{align*}
y^{\prime }+\cos \left (x \right ) y&=y^{n} \sin \left (2 x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
62.892 |
|
| \begin{align*}
y-x y^{2} \ln \left (x \right )+y^{\prime } x&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
45.276 |
|
| \begin{align*}
y y^{\prime } x -y^{2}&=x^{4} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
118.464 |
|
| \begin{align*}
y^{2} y^{\prime } x -y^{3}&=\frac {x^{4}}{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
140.303 |
|
| \begin{align*}
x^{2}+y^{2}-y y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
112.602 |
|
| \begin{align*}
y+x y^{2}-y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
115.730 |
|
| \begin{align*}
2 y y^{\prime }+2 x +x^{2}+y^{2}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
79.171 |
|
| \begin{align*}
2 y y^{\prime }&=1 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
20.382 |
|
| \begin{align*}
3 y^{\prime }&=\frac {4 x}{y^{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
163.388 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
94.763 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}&=\frac {2 y^{2}+1}{x +1} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
138.428 |
|
| \begin{align*}
4 y^{4}-1+12 x y^{3} y^{\prime }&=0 \\
y \left (1\right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
138.052 |
|
| \begin{align*}
y x +x^{2} y^{\prime }&=-\frac {1}{y^{{3}/{2}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
138.254 |
|
| \begin{align*}
y^{\prime }+y x&=x y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
86.240 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y}+\frac {y}{x} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
126.088 |
|
| \begin{align*}
y^{\prime }+\frac {y}{x}&=\frac {1}{x^{4} y^{{3}/{4}}} \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✗ |
142.313 |
|
| \begin{align*}
y^{\prime }&=-\frac {y^{2}}{x}+\frac {2 y}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
152.790 |
|
| \begin{align*}
x^{3} y^{\prime }&=x^{2} y-y^{3} \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
231.137 |
|
| \begin{align*}
y^{\prime }+\frac {2 y}{x}&=\frac {3 y^{2}}{x} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
133.385 |
|
| \begin{align*}
x +y y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
121.511 |
|
| \begin{align*}
y^{\prime }&=\frac {x}{y} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
146.290 |
|
| \begin{align*}
x^{2}+y^{2} y^{\prime }&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
73.849 |
|
| \begin{align*}
\left (x^{2}-1\right ) y^{\prime }+2 x y^{2}&=0 \\
y \left (0\right ) &= 1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
40.237 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
y \left (2\right ) &= 0 \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
37.766 |
|
| \begin{align*}
y^{\prime } x +y&=y^{2} \\
y \left (1\right ) &= {\frac {1}{2}} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
90.375 |
|
| \begin{align*}
2 x^{2} y y^{\prime }+y^{2}&=2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
70.560 |
|
| \begin{align*}
y^{\prime }-x y^{2}&=2 y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
63.991 |
|
| \begin{align*}
x x^{\prime }+t&=1 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
76.212 |
|
| \begin{align*}
3 y^{2} y^{\prime }+16 x&=2 x y^{3} \\
y \left (\infty \right ) &= 2 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✗ |
37.335 |
|
| \begin{align*}
y^{2}-2 y x +x^{2} y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
119.084 |
|
| \begin{align*}
2 x^{3} y^{\prime }&=\left (2 x^{2}-y^{2}\right ) y \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
195.714 |
|
| \begin{align*}
2 x^{2} y^{\prime }&=y^{3}+y x \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
107.335 |
|
| \begin{align*}
2 y^{\prime } x +\left (1+x^{2} y^{4}\right ) y&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
147.201 |
|
| \begin{align*}
2 y+y^{\prime }&=y^{2} {\mathrm e}^{x} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
41.951 |
|
| \begin{align*}
\left (x +1\right ) \left (y^{\prime }+y^{2}\right )&=-y \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
35.257 |
|
| \begin{align*}
y^{\prime }&=y^{4} \cos \left (x \right )+\tan \left (x \right ) y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
111.973 |
|
| \begin{align*}
y^{2} y^{\prime } x&=x^{2}+y^{3} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
199.184 |
|
| \begin{align*}
y y^{\prime } x&=x +y^{2} \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
141.356 |
|
| \begin{align*}
y^{\prime } x -2 \sqrt {y}\, x^{2}&=4 y \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
133.984 |
|
| \begin{align*}
y^{\prime } x +2 y+x^{5} y^{3} {\mathrm e}^{x}&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
51.997 |
|
| \begin{align*}
2 y^{\prime }-\frac {x}{y}&=\frac {x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
34.318 |
|
| \begin{align*}
\left (x +1\right ) \left (y y^{\prime }-1\right )&=y^{2} \\
\end{align*} |
[[_1st_order, _with_linear_symmetries], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
79.336 |
|
| \begin{align*}
1+y^{2} \sin \left (2 x \right )-2 y \cos \left (x \right )^{2} y^{\prime }&=0 \\
\end{align*} |
[_exact, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
74.168 |
|
| \begin{align*}
x^{2}+y^{2}+x +y y^{\prime }&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
77.332 |
|
| \begin{align*}
x y^{2} \left (y^{\prime } x +y\right )&=1 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
154.372 |
|
| \begin{align*}
y-\frac {1}{x}+\frac {y^{\prime }}{y}&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
144.726 |
|
| \begin{align*}
y^{\prime }&=y^{2}+2 y x \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
28.121 |
|
| \begin{align*}
y^{\prime }&=3 y^{{2}/{3}} \\
\end{align*} |
[_quadrature] |
✓ |
✓ |
✓ |
✓ |
58.583 |
|
| \begin{align*}
2 x y^{2}-y+y^{\prime } x&=0 \\
\end{align*} |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
109.142 |
|
| \begin{align*}
y-y^{\prime }&=y^{\prime } x +y^{2} \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
102.121 |
|
| \begin{align*}
x^{2} y^{\prime }&=y \left (x +y\right ) \\
\end{align*} |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.950 |
|
| \begin{align*}
2 y y^{\prime } x^{3}+3 y^{2} x^{2}+7&=0 \\
\end{align*} |
[[_homogeneous, ‘class G‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
80.420 |
|
| \begin{align*}
y^{\prime }+y x -x y^{3}&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
122.466 |
|
| \begin{align*}
\left (-x^{2}+1\right ) y^{\prime }-2 x y^{2}&=y x \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
108.947 |
|
| \begin{align*}
y^{\prime }+y&=x y^{3} \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
56.910 |
|
| \begin{align*}
x y^{2}-x +\left (y x +y\right ) y^{\prime }&=0 \\
\end{align*} |
[_separable] |
✓ |
✓ |
✓ |
✓ |
94.178 |
|
| \begin{align*}
y y^{\prime }+\cot \left (x \right ) y^{2}&=\cos \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
73.139 |
|
| \begin{align*}
y^{\prime }+x y^{{1}/{3}}&=3 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.839 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
86.427 |
|
| \begin{align*}
y^{\prime }&=\frac {x \,{\mathrm e}^{2 x}}{y}+y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.236 |
|
| \begin{align*}
y^{\prime } x&=2 \sqrt {y}\, \cos \left (x \right )-2 y \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
111.248 |
|
| \begin{align*}
\frac {x y^{\prime }}{y}+2 x y \ln \left (x \right )+1&=0 \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
72.647 |
|
| \begin{align*}
y^{2} y^{\prime }+x^{2} \sin \left (x \right )^{3}&=y^{3} \cot \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
90.662 |
|
| \begin{align*}
\left (y^{\prime }-x \sqrt {y}\right ) \left (x^{2}-1\right )&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
59.714 |
|
| \begin{align*}
y^{2}&=\left (y y^{\prime } x +1\right ) \ln \left (x \right ) \\
\end{align*} |
[_Bernoulli] |
✓ |
✓ |
✓ |
✓ |
81.452 |
|
| \begin{align*}
x \left (-1+x \right ) y^{\prime }+y^{3}&=y x \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
66.277 |
|
| \begin{align*}
y^{\prime }&=\frac {y^{2}-x}{2 \left (x +1\right ) y} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✗ |
✓ |
45.106 |
|
| \begin{align*}
y^{\prime }-8 x \sqrt {y}&=\frac {4 x y}{x^{2}-1} \\
\end{align*} |
[_rational, _Bernoulli] |
✓ |
✓ |
✓ |
✓ |
60.970 |
|