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 : Monday, January 27, 2025 at 02:42:14 PM
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*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

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

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

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