Internal problem ID [5802]
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: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y \left (x y+1\right )+\left (1-x y\right ) x y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve(y(x)*(1+x*y(x))+(1-x*y(x))*x*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x^{2}}\right ) x} \]
✓ Solution by Mathematica
Time used: 6.096 (sec). Leaf size: 35
DSolve[y[x]*(1+x*y[x])+(1-x*y[x])*x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{x W\left (\frac {e^{-1+\frac {9 c_1}{2^{2/3}}}}{x^2}\right )} \\ y(x)\to 0 \\ \end{align*}