Internal problem ID [5750]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {L i^{\prime }+R i-E_{0} \left (\delta \relax (t )\right )=0} \end {gather*} With initial conditions \begin {align*} [i \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 21
dsolve([L*diff(i(t),t)+R*i(t)=E__0*Dirac(t),i(0) = 0],i(t), singsol=all)
\[ i \relax (t ) = \frac {E_{0} {\mathrm e}^{-\frac {R t}{L}} \left (2 \theta \relax (t )-1\right )}{2 L} \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 26
DSolve[{L*i'[t]+R*i[t]==E0*DiracDelta[t],{i[0]==0}},i[t],t,IncludeSingularSolutions -> True]
\begin{align*} i(t)\to \frac {\text {E0} (\theta (t)-\theta (0)) e^{-\frac {R t}{L}}}{L} \\ \end{align*}