50.3.19 problem 3(c)

Internal problem ID [7843]
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)
Date solved : Monday, January 27, 2025 at 03:25:31 PM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 22

DSolve[x*D[y[x],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*}