43.2.7 problem 3

Internal problem ID [8883]
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 : Tuesday, September 30, 2025 at 05:58:53 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 21

ode:=L*diff(y(x),x)+R*y(x) = E; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {E \left (1-{\mathrm e}^{-\frac {R x}{L}}\right )}{R} \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 23

ode=L*D[y[x],x]+R*y[x]==e0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\text {e0}-\text {e0} e^{-\frac {R x}{L}}}{R} \end{align*}

✓ Sympy. Time used: 0.087 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
E = symbols("E") 
L = symbols("L") 
R = symbols("R") 
y = Function("y") 
ode = Eq(L*Derivative(y(x), x) + R*y(x) - E,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {R x}{L}} + \frac {e}{R} \]