66.8.27 problem 40

Internal problem ID [16078]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 40
Date solved : Thursday, October 02, 2025 at 10:40:58 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{2}-2 y+1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 13

ode:=diff(y(t),t) = y(t)^2-2*y(t)+1; 
ic:=[y(0) = 2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {t -2}{t -1} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 14

ode=D[y[t],t]== y[t]^2-2*y[t]+1; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {t-2}{t-1} \end{align*}

✓ Sympy. Time used: 0.107 (sec). Leaf size: 8

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

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