71.6.3 problem 3

Internal problem ID [14409]
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 : 3
Date solved : Tuesday, January 28, 2025 at 06:29:57 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1-y \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 10

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

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

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 12

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

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