49.2.4 problem 1(d)

Internal problem ID [7594]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 03:06:58 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} 3 y^{\prime }+y&=2 \,{\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 17

dsolve(3*diff(y(x),x)+y(x)=2*exp(-x),y(x), singsol=all)
 

\[ y = -{\mathrm e}^{-x}+{\mathrm e}^{-\frac {x}{3}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 23

DSolve[3*D[y[x],x]+y[x]==2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (-1+c_1 e^{2 x/3}\right ) \]