49.2.10 problem 7

Internal problem ID [7600]
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 : 7
Date solved : Monday, January 27, 2025 at 03:07:07 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 32

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

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