44.5.48 problem 44

Internal problem ID [7110]
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, February 04, 2025 at 12:14:47 AM
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*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

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

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

\[ y(x)\to \frac {x-101}{x-100} \]