72.8.27 problem 40

Internal problem ID [14791]
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 : Tuesday, January 28, 2025 at 07:15:38 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*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 14

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

\[ y(t)\to \frac {t-2}{t-1} \]