71.6.7 problem 7

Internal problem ID [14413]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 06:30:09 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=-2 y+y^{2} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 14

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

\[ y = \frac {2}{1+{\mathrm e}^{2 x}} \]

✓ Solution by Mathematica

Time used: 0.009 (sec). Leaf size: 16

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

\[ y(x)\to \frac {2}{e^{2 x}+1} \]