44.4.31 problem 12 (a)

Internal problem ID [7044]
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 2.1 Solution curves without a solution. Exercises 2.1 at page 44
Problem number : 12 (a)
Date solved : Sunday, March 30, 2025 at 11:36:19 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=1-\frac {y}{x} \end{align*}

With initial conditions

\begin{align*} y \left (-\frac {1}{2}\right )&=2 \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 13

ode:=diff(y(x),x) = 1-y(x)/x; 
ic:=y(-1/2) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x}{2}-\frac {9}{8 x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 18

ode=D[y[x],x]==1-y[x]/x; 
ic={y[-1/2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x}{2}-\frac {9}{8 x} \]

✓ Sympy. Time used: 0.210 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - 1 + y(x)/x,0) 
ics = {y(-1/2): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x}{2} - \frac {9}{8 x} \]