14.3.2 problem Problem 2

Internal problem ID [3611]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 2
Date solved : Tuesday, September 30, 2025 at 06:48:31 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 y}{x}&=5 x^{2} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

ode:=diff(y(x),x)+2*y(x)/x = 5*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{5}+c_1}{x^{2}} \]

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

ode=D[y[x],x]+2/x*y[x]==5*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x^5+c_1}{x^2} \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x**2 + Derivative(y(x), x) + 2*y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + x^{5}}{x^{2}} \]