44.5.44 problem 40 (c)

Internal problem ID [7106]
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 (c)
Date solved : Tuesday, February 04, 2025 at 12:14:39 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 11

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

\[ y = \frac {1}{1+2 x} \]

✓ Solution by Mathematica

Time used: 0.277 (sec). Leaf size: 12

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

\[ y(x)\to \frac {1}{2 x+1} \]