44.5.49 problem 45

Internal problem ID [7111]
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 : 45
Date solved : Tuesday, February 04, 2025 at 12:14:48 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: 0.028 (sec). Leaf size: 12

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

\[ y = 1+\frac {\tan \left (\frac {x}{10}\right )}{10} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 17

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

\[ y(x)\to \frac {1}{10} \tan \left (\frac {x}{10}\right )+1 \]