64.5.28 problem 28

Internal problem ID [13341]
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 : 28
Date solved : Tuesday, January 28, 2025 at 05:31:11 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 5 & 0\le x <10 \\ 1 & 10\le x \end {array}\right . \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.888 (sec). Leaf size: 40

dsolve([diff(y(x),x)+y(x)=piecewise(0<=x and x<10,5,x>=10,1),y(0) = 6],y(x), singsol=all)
 

\[ y = \left \{\begin {array}{cc} 6 \,{\mathrm e}^{-x} & x <0 \\ {\mathrm e}^{-x}+5 & x <10 \\ {\mathrm e}^{-x}+1+4 \,{\mathrm e}^{10-x} & 10\le x \end {array}\right . \]

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 45

DSolve[{D[y[x],x]+y[x]==Piecewise[{{5,0<=x<10},{1,x>=10}}],{y[0]==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 6 e^{-x} & x\leq 0 \\ e^{-x} \left (1+4 e^{10}+e^x\right ) & x>10 \\ 5+e^{-x} & \text {True} \\ \end {array} \\ \end {array} \]