38.6.10 problem 10

Internal problem ID [8440]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 05:36:49 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ y = \frac {3}{2}+\frac {c_1}{x^{2}} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {3}{2}+\frac {c_1}{x^2}\\ y(x)&\to \frac {3}{2} \end{align*}

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

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

\[ y{\left (x \right )} = \frac {C_{1}}{x^{2}} + \frac {3}{2} \]