49.2.1 problem 1(a)

Internal problem ID [7591]
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(a)
Date solved : Monday, January 27, 2025 at 03:06:54 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-2 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 12

dsolve(diff(y(x),x)-2*y(x)=1,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 24

DSolve[D[y[x],x]-2*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2}+c_1 e^{2 x} \\ y(x)\to -\frac {1}{2} \\ \end{align*}