49.3.8 problem 8

Internal problem ID [7608]
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 : 8
Date solved : Monday, January 27, 2025 at 03:07:23 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=b \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(diff(y(x),x)+2*y(x)=b(x),y(x), singsol=all)
 

\[ y = \left (\int b \left (x \right ) {\mathrm e}^{2 x}d x +c_{1} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 31

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

\[ y(x)\to e^{-2 x} \left (\int _1^xe^{2 K[1]} b(K[1])dK[1]+c_1\right ) \]