44.6.29 problem 29

Internal problem ID [7173]
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, February 04, 2025 at 12:44:08 AM
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*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 26

dsolve([L*diff(i(t),t)+R*i(t)=E,i(0) = i__0],i(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 34

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

\[ i(t)\to \frac {e^{-\frac {R t}{L}} \left (e \left (e^{\frac {R t}{L}}-1\right )+\text {i0} R\right )}{R} \]