29.20.20 problem 567

Internal problem ID [5161]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 20
Problem number : 567
Date solved : Monday, January 27, 2025 at 10:16:36 AM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 18

dsolve(x*(1-x*y(x))*diff(y(x),x)+(1+x*y(x))*y(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: 5.972 (sec). Leaf size: 35

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