64.5.27 problem 27

Internal problem ID [13340]
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 : 27
Date solved : Tuesday, January 28, 2025 at 05:31:09 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.787 (sec). Leaf size: 38

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

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

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 38

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

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