49.2.7 problem 3

Internal problem ID [7597]
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 : 3
Date solved : Monday, January 27, 2025 at 03:07:02 PM
CAS classification : [_quadrature]

\begin{align*} L y^{\prime }+R y&=E \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(L*diff(y(x),x)+R*y(x)=E,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 23

DSolve[L*D[y[x],x]+R*y[x]==e0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\text {E0}-\text {E0} e^{-\frac {R x}{L}}}{R} \]