44.5.47 problem 43

Internal problem ID [7109]
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 : 43
Date solved : Tuesday, February 04, 2025 at 12:14:46 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 5

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

\[ y = 1 \]

✓ Solution by Mathematica

Time used: 0.001 (sec). Leaf size: 6

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

\[ y(x)\to 1 \]