50.17.19 problem 2(d) solving using series

Internal problem ID [8090]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 2(d) solving using series
Date solved : Monday, January 27, 2025 at 03:43:33 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)+(1/x)*y(x)=x,y(x), singsol=all)
 

\[ y = \frac {x^{3}+3 c_{1}}{3 x} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 19

DSolve[D[y[x],x]+1/x*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^2}{3}+\frac {c_1}{x} \]