49.2.2 problem 1(b)

Internal problem ID [7592]
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(b)
Date solved : Monday, January 27, 2025 at 03:06:55 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {{\mathrm e}^{x}}{2}+c_{1} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 21

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

\[ y(x)\to \frac {e^x}{2}+c_1 e^{-x} \]