64.5.29 problem 29

Internal problem ID [13342]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 05:31:12 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} {\mathrm e}^{-x} & 0\le x <2 \\ {\mathrm e}^{-2} & 2\le x \end {array}\right . \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.886 (sec). Leaf size: 35

dsolve([diff(y(x),x)+y(x)=piecewise(0<=x and x<2,exp(-x),x>=2,exp(-2)),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 40

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

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