44.5.50 problem 46

Internal problem ID [7112]
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 : 46
Date solved : Tuesday, February 04, 2025 at 12:14:49 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (y-1\right )^{2}-\frac {1}{100} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.037 (sec). Leaf size: 23

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

\[ y = \frac {11+9 \,{\mathrm e}^{\frac {x}{5}}}{10 \,{\mathrm e}^{\frac {x}{5}}+10} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 30

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

\[ y(x)\to \frac {9 e^{x/5}+11}{10 e^{x/5}+10} \]