44.5.45 problem 40 (d)

Internal problem ID [7107]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 40 (d)
Date solved : Tuesday, February 04, 2025 at 12:14:41 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (2\right )&={\frac {1}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 13

dsolve([x*diff(y(x),x)=y(x)^2-y(x),y(2) = 1/4],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.090 (sec). Leaf size: 14

DSolve[{x*D[y[x],x]==y[x]^2-y[x],{y[2]==1/4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2}{3 x+2} \]