44.5.52 problem 47 (b)

Internal problem ID [7114]
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 : 47 (b)
Date solved : Tuesday, February 04, 2025 at 12:15:03 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y-y^{3} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 14

dsolve([diff(y(x),x)=y(x)-y(x)^3,y(0) = 1/2],y(x), singsol=all)
 

\[ y = \frac {1}{\sqrt {3 \,{\mathrm e}^{-2 x}+1}} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 20

DSolve[{D[y[x],x]==y[x]-y[x]^3,{y[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^x}{\sqrt {e^{2 x}+3}} \]