50.8.9 problem 2(a)

Internal problem ID [7925]
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. Problems for Review and Discovery. Page 53
Problem number : 2(a)
Date solved : Monday, January 27, 2025 at 03:32:38 PM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

dsolve([x*diff(y(x),x)-y(x)=2*x,y(1) = 0],y(x), singsol=all)
 

\[ y = 2 \ln \left (x \right ) x \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 10

DSolve[{x*D[y[x],x]-y[x]==2*x,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 x \log (x) \]