50.24.5 problem 7(b)

Internal problem ID [8171]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 7. Laplace Transforms. Section 7.5 The Unit Step and Impulse Functions. Page 303
Problem number : 7(b)
Date solved : Monday, January 27, 2025 at 03:45:11 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} L i^{\prime }+R i&=E_{0} \delta \left (t \right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.545 (sec). Leaf size: 17

dsolve([L*diff(i(t),t)+R*i(t)=E__0*Dirac(t),i(0) = 0],i(t), singsol=all)
 

\[ i = \frac {{\mathrm e}^{-\frac {R t}{L}} E_{0}}{L} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 26

DSolve[{L*D[i[t],t]+R*i[t]==e0*DiracDelta[t],{i[0]==0}},i[t],t,IncludeSingularSolutions -> True]
 

\[ i(t)\to \frac {\text {e0} (\theta (t)-\theta (0)) e^{-\frac {R t}{L}}}{L} \]