Consider the differential equation
$${{{d^2}y\left( t \right)} \over {d{t^2}}} + 2{{dy\left( t \right)} \over {dt}} + y\left( t \right) = \delta \left( t \right)$$
with $$y\left( t \right)\left| {_{t = 0} = - 2} \right.$$ and $${{dy} \over {dt}}\left| {_{t = 0}} \right. = 0.$$

The numerical value of $${{dy} \over {dt}}\left| {_{t = 0}.} \right.$$ is

Given $$f(t)$$ and $$g(t)$$ as shown below

$$g(t)$$ can be expressed as

Given $$f(t)$$ and $$g(t)$$ as shown below

The laplace transform of $$g(t)$$ is