solving $\dot{x}(t) + x(t) = \delta (t) $ Using Laplace transform for
$x(0) = 1$, we get:

$sX(s)-1 + X(s) = 1$

$X(s) = \frac{2}{s+1}$

so, $x(t) = 2e^{-t}$

However, evaluating at t=0,
$x(0) = 2 \neq 1$
This disagrees with the initial condition. What went wrong here?