89.5.29 problem 29

Internal problem ID [24379]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 29
Date solved : Thursday, October 02, 2025 at 10:22:42 PM
CAS classification : [_quadrature]

\begin{align*} L i^{\prime }+R i&=e \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 21

ode:=L*diff(i(t),t)+R*i(t) = e; 
ic:=[i(0) = 0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = \frac {e \left (1-{\mathrm e}^{-\frac {R t}{L}}\right )}{R} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 23

ode=L*D[i[t],t]+R*i[t]== e; 
ic={i[0]==0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to \frac {e-e e^{-\frac {R t}{L}}}{R} \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
L = symbols("L") 
R = symbols("R") 
e = symbols("e") 
i = Function("i") 
ode = Eq(L*Derivative(i(t), t) + R*i(t) - e,0) 
ics = {i(0): 0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = \frac {e}{R} - \frac {e e^{- \frac {R t}{L}}}{R} \]