44.6.42 problem 42

Internal problem ID [7186]
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 : 42
Date solved : Tuesday, February 04, 2025 at 12:45:31 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+\left (\left \{\begin {array}{cc} 1 & 0\le x \le 2 \\ 5 & 2<x \end {array}\right .\right ) y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.275 (sec). Leaf size: 27

dsolve([diff(y(x),x)+piecewise(0<=x and x<=2,1,x>2,5)*y(x)=0,y(0) = 4],y(x), singsol=all)
 

\[ y = 4 \left (\left \{\begin {array}{cc} 1 & x <0 \\ {\mathrm e}^{-x} & x <2 \\ {\mathrm e}^{-5 x +8} & 2\le x \end {array}\right .\right ) \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 32

DSolve[{D[y[x],x]+Piecewise[{ {1,0<=x<=2},{5,x>2}}]*y[x]==0,{y[0]==4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 4 & x\leq 0 \\ 4 e^{8-5 x} & x>2 \\ 4 e^{-x} & \text {True} \\ \end {array} \\ \end {array} \]