2.7 problem 3

Internal problem ID [5176]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {L y^{\prime }+R y-E=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 20

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

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

Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 23

DSolve[L*y'[x]+R*y[x]==E0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\text {E0}-\text {E0} e^{-\frac {R x}{L}}}{R} \\ \end{align*}