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MATH 220 E1 ~~~~~~ QUIZ \#9  ~~~~~  (20 points)\\*[1em]
(12 minutes, 12 March 1999, Sections 7.5-7.7)
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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:}\\*[2em]
{\B \hspace*{2em}\boldmath{$y^{\prime\prime}(t)+5y^{\prime}(t)+6y(t) = 7 u(t-4)$}\\*[1em]
\hspace*{4.5em}\boldmath{$y(0)=0;~~ y^{\prime}(0)=2;$}\\*[2em]
Hint: \boldmath{$\LC[f(t-a)u(t-a)](s)=e^{-as}F(s);~~ \\*[1ex]
\LC[f*g](s)=F(s)\cdot G(s);\\*[1ex]
\frac{1}{s(s+a)(s+b)}=\frac{1}{b-a}\left(
\frac{1}{a}\left(\frac{1}{s}-\frac{1}{s+a}\right)
-\frac{1}{b}\left(\frac{1}{s}-\frac{1}{s+b}\right)\right);
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