17.18 problem 2(c) solving directly

Internal problem ID [5668]

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(c) solving directly.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_linear]

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

Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x), singsol=all)
 

\[ y \relax (x ) = \left (\frac {x^{2}}{2}+c_{1}\right ) x \]

Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 17

DSolve[y'[x]-1/x*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {x^3}{2}+c_1 x \\ \end{align*}