38.6.29 problem 29

Internal problem ID [8459]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 05:37:26 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 26

ode:=L*diff(i(t),t)+R*i(t) = E; 
ic:=[i(0) = i__0]; 
dsolve([ode,op(ic)],i(t), singsol=all);
 

\[ i = \frac {\left (i_{0} R -E \right ) {\mathrm e}^{-\frac {R t}{L}}+E}{R} \]

✓ Mathematica. Time used: 0.034 (sec). Leaf size: 34

ode=L*D[i[t],t]+R*i[t]==e; 
ic={i[0]==i0}; 
DSolve[{ode,ic},i[t],t,IncludeSingularSolutions->True]
 

\begin{align*} i(t)&\to \frac {e^{-\frac {R t}{L}} \left (e \left (e^{\frac {R t}{L}}-1\right )+\text {i0} R\right )}{R} \end{align*}

✓ Sympy. Time used: 0.097 (sec). Leaf size: 22

from sympy import * 
t = symbols("t") 
E = symbols("E") 
L = symbols("L") 
R = symbols("R") 
i = Function("i") 
ode = Eq(L*Derivative(i(t), t) + R*i(t) - E,0) 
ics = {i(0): i__0} 
dsolve(ode,func=i(t),ics=ics)
 

\[ i{\left (t \right )} = \frac {\left (R i^{0} - e\right ) e^{- \frac {R t}{L}}}{R} + \frac {e}{R} \]