64.6.22 problem 22

Internal problem ID [13372]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 05:33:19 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le x <2 \\ 0 & 0<x \end {array}\right . \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.784 (sec). Leaf size: 36

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

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

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 39

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

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