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{\LARGE
\begin{center}
MATH 220 E1 ~~~~~~ QUIZ \#10  ~~~~~  (20 points)\\*[1em]
(12 minutes, 26 March 1999, Sections of Chapter 7)
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NAME:
\\*[0.5em]
SOCIAL SECURITY NUMBER (SSN):
\\*[0.5em]
DISCUSSION TIME AND DAY (DT\&D):
\\*[1.5em]
{\B 1. Find the Solution to the IVP Using the Laplace (\boldmath{$\LC$}) and
its Inverse (\boldmath{$\LCI$}) Transform:}\\*[1em]
{\B \hspace*{2em}\boldmath{$y^{\prime\prime}(t))+\pi^2 y(t) = 10\pi\delta(t-3)$}\\*[1em]
\hspace*{2.5em}\boldmath{$y(0)=12;~~ y^{\prime}(0)=14\pi;$}\\*[1em]}
{\I\{No Calculators Needed or Allowed\}}\\*[2.0ex]
{\I Brief Table of Laplace Transforms:}\\*[2.0ex]
\boldmath{$\LC[f(t-a)\delta(t-a)](s)=e^{\ML{-as}}f(0),~~ a>0;~~ $}\\*[2.0ex]
\boldmath{$\LC[f(t-a)u(t-a)](s)=e^{\ML{-as}}F(s),~~ a>0;~~$} \\*[2.0ex]
\boldmath{$\LCI\left[\frac{\ML{As+B}}{\ML{(s-a)}^2+\ML{b}^2}\right](t)
=Ae^{\ML{at}}\cos(\ML{bt})
+\frac{\ML{(B+aA)}}{\ML{b}}e^{\ML{at}}\sin(\ML{bt})$}.
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