50.17.17 problem 2(c) solving using series

Internal problem ID [8088]
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 using series
Date solved : Monday, January 27, 2025 at 03:43:30 PM
CAS classification : [_linear]

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

Using series method with expansion around

\begin{align*} 0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 24

Order:=8; 
dsolve(diff(y(x),x)-(1/x)*y(x)=x^2,y(x),type='series',x=0);
 

\[ y = c_{1} x \left (1+\operatorname {O}\left (x^{8}\right )\right )+x^{3} \left (\frac {1}{2}+\operatorname {O}\left (x^{5}\right )\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 15

AsymptoticDSolveValue[D[y[x],x]-1/x*y[x]==x^2,y[x],{x,0,"8"-1}]
 

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