3.19 problem 3(c)

Internal problem ID [5422]

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 1.4 First Order Linear Equations. Page 15
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]

Solve \begin {gather*} \boxed {x y^{\prime }+y-y^{2} x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 17

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

\[ y \relax (x ) = -\frac {1}{\left (\ln \relax (x )-c_{1}\right ) x} \]

Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 22

DSolve[x*y'[x]+y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{-x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}