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 : Sunday, March 30, 2025 at 11:42:36 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*}

✓ Maple. Time used: 0.076 (sec). Leaf size: 13

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

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 14

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

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

✓ Sympy. Time used: 0.323 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) - y(x)**2 + y(x),0) 
ics = {y(2): 1/4} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {1}{- \frac {3 x}{2} - 1} \]