Internal problem ID [6116]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]
\[ \boxed {y^{\prime }-\frac {y^{2}}{x y-x^{2}}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 17
dsolve(diff(y(x),x)=y(x)^2/(x*y(x)-x^2),y(x), singsol=all)
\[ y \left (x \right ) = -x \operatorname {LambertW}\left (-\frac {{\mathrm e}^{-c_{1}}}{x}\right ) \]
✓ Solution by Mathematica
Time used: 2.335 (sec). Leaf size: 25
DSolve[y'[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*}