58.5.1 problem 1

Internal problem ID [14595]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:43:46 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {3 y}{x}&=6 x^{2} \end{align*}

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

ode:=diff(y(x),x)+3*y(x)/x = 6*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{6}+c_1}{x^{3}} \]

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 15

ode=D[y[x],x]+3*y[x]/x==6*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^6+c_1}{x^3} \end{align*}

✓ Sympy. Time used: 0.101 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**2 + Derivative(y(x), x) + 3*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{6}}{x^{3}} \]