44.5.42 problem 40 (a)

Internal problem ID [7104]
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 (a)
Date solved : Tuesday, February 04, 2025 at 12:14:35 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.039 (sec). Leaf size: 37

dsolve([x*diff(y(x),x)=y(x)^2-y(x),y(0) = 1],y(x), singsol=all)
 

\begin{align*} y &= 1 \\ y &= \frac {c_1}{c_1 -x} \\ y &= \frac {c_1}{x +c_1} \\ y &= \frac {1}{c_1 x +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

DSolve[{x*D[y[x],x]==y[x]^2-y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 1 \]