50.1.12 problem 1(m)

Internal problem ID [7784]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 1(m)
Date solved : Monday, January 27, 2025 at 03:22:52 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {y^{2}}{y x -x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 2.143 (sec). Leaf size: 25

DSolve[D[y[x],x]==y[x]^2/(x*y[x]-x^2),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*}