38.5.48 problem 44

Internal problem ID [8396]
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 : 44
Date solved : Tuesday, September 30, 2025 at 05:34:42 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {101}{100}} \\ \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 13

ode:=diff(y(x),x) = (y(x)-1)^2; 
ic:=[y(0) = 101/100]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x -101}{x -100} \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 14

ode=D[y[x],x]==(y[x]-1)^2; 
ic={y[0]==101/100}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x-101}{x-100} \end{align*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(y(x) - 1)**2 + Derivative(y(x), x),0) 
ics = {y(0): 101/100} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {101 - x}{100 - x} \]