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 : Wednesday, March 05, 2025 at 05:29:40 AM
CAS classification : [_linear]

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

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

ode:=diff(y(x),x)+y(x)/x = x; 
dsolve(ode,y(x), singsol=all);
 

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

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

ode=D[y[x],x]+1/x*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.166 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x + Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{3}}{3}}{x} \]