44.6.38 problem 38

Internal problem ID [7182]
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 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 38
Date solved : Tuesday, February 04, 2025 at 12:45:02 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x \le 1 \\ -1 & 1<x \end {array}\right . \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.192 (sec). Leaf size: 29

dsolve([diff(y(x),x)+y(x)=piecewise(0<=x and x<=1,1,x>1,-1),y(0) = 1],y(x), singsol=all)
 

\[ y = \left \{\begin {array}{cc} {\mathrm e}^{-x} & x <0 \\ 1 & x <1 \\ -1+2 \,{\mathrm e}^{1-x} & 1\le x \end {array}\right . \]

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 35

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

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} e^{-x} & x\leq 0 \\ 1 & 0<x\leq 1 \\ -1+2 e^{1-x} & \text {True} \\ \end {array} \\ \end {array} \]