Internal problem ID [3318]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 20
Problem number: 576.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, [_Abel, 2nd type, class B]]
Solve \begin {gather*} \boxed {x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.017 (sec). Leaf size: 18
dsolve(x*(1-2*x*y(x))*diff(y(x),x)+(1+2*x*y(x))*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {1}{2 \LambertW \left (-\frac {c_{1}}{2 x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 135.705 (sec). Leaf size: 32
DSolve[x(1-2 x y[x])y'[x]+(1+2 x y[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{2 x \text {ProductLog}\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ \end{align*}