81.6.8 problem 7-8

Internal problem ID [21554]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 7. Linear Differential Equations. Page 101.
Problem number : 7-8
Date solved : Thursday, October 02, 2025 at 07:48:02 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x}&=3 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=diff(y(x),x)+y(x)/x = 3*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}+c_1}{x} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 15

ode=D[y[x],x]+ y[x]/x==3*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.085 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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