49.3.3 problem 1(c)

Internal problem ID [7603]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1. Introduction– Linear equations of First Order. Page 45
Problem number : 1(c)
Date solved : Monday, January 27, 2025 at 03:07:12 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 22

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

\begin{align*} y(x)\to 3+c_1 e^{-e^x} \\ y(x)\to 3 \\ \end{align*}