80.3.1 problem 1

Internal problem ID [18545]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 11:55:21 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{2}&=x \left (y-x \right ) y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve(y(x)^2=x*(y(x)-x)*diff(y(x),x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.010 (sec). Leaf size: 25

DSolve[y[x]^2==x*(y[x]-x)*D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x W\left (-\frac {e^{-c_1}}{x}\right ) \\ y(x)\to 0 \\ \end{align*}