Internal problem ID [5043]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 44.
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 {y+x \left (1+2 x y\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 18
dsolve(y(x)+x*(2*x*y(x)+1)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {1}{2 \LambertW \left (\frac {c_{1}}{2 x}\right ) x} \]
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 36
DSolve[y[x]+x*(2*x*y[x]+1)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2 x \text {ProductLog}\left (\frac {e^{\frac {1}{2} \left (-2-9 \sqrt [3]{-2} c_1\right )}}{x}\right )} \\ \end{align*}