47.2.54 problem 50

Internal problem ID [7470]
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
Date solved : Monday, January 27, 2025 at 03:01:27 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y \left (1+y x \right )+\left (1-y x \right ) x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (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)
 

\[ y = -\frac {1}{\operatorname {LambertW}\left (-\frac {c_{1}}{x^{2}}\right ) x} \]

✓ Solution by Mathematica

Time used: 5.777 (sec). Leaf size: 35

DSolve[y[x]*(1+x*y[x])+(1-x*y[x])*x*D[y[x],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*}