Answer
$s(t)=3e^{t}+\displaystyle \frac{t^{2}}{2}$
Work Step by Step
The given information is that $s(0)=3$
$s(t)=3e^{t}+\displaystyle \frac{t^{2}}{2}+C\qquad $ insert the given data to find $C$
$3=3e^{0}+0+C$
$3=3+C$
$C=0$,
Thus,
$s(t)=3e^{t}+\displaystyle \frac{t^{2}}{2}$
