44.6.37 problem 37

Internal problem ID [7181]
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 : 37
Date solved : Tuesday, February 04, 2025 at 12:44:58 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=\left \{\begin {array}{cc} 1 & 0\le x \le 3 \\ 0 & 3<x \end {array}\right . \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.319 (sec). Leaf size: 38

dsolve([diff(y(x),x)+2*y(x)=piecewise(0<=x and x<=3,1,x>3,0),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\left (\left \{\begin {array}{cc} 0 & x <0 \\ 1-{\mathrm e}^{-2 x} & x <3 \\ {\mathrm e}^{6-2 x}-{\mathrm e}^{-2 x} & 3\le x \end {array}\right .\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 46

DSolve[{D[y[x],x]+2*y[x]==Piecewise[{ {1,0<=x<=3},{0,x>3}}],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & x\leq 0 \\ \frac {1}{2}-\frac {e^{-2 x}}{2} & 0<x\leq 3 \\ \frac {1}{2} e^{-2 x} \left (-1+e^6\right ) & \text {True} \\ \end {array} \\ \end {array} \]