36.2.18 problem 18

Internal problem ID [6311]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises. page 54
Problem number : 18
Date solved : Monday, January 27, 2025 at 01:55:49 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y-{\mathrm e}^{-x}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {4}{3}} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve([diff(y(x),x)+4*y(x)-exp(-x)=0,y(0) = 4/3],y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left ({\mathrm e}^{3 x}+3\right ) {\mathrm e}^{-4 x}}{3} \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 21

DSolve[{D[y[x],x]+4*y[x]-Exp[-x]==0,{y[0]==4/3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{3} e^{-4 x} \left (e^{3 x}+3\right ) \]