Interpretation of ODE with Dirac delta input and initial conditions at $t=0$

Question

Let's consider the following IVP:

$y'' + 2y' + 10 y = \delta(t)$

$y(0) = y'(0) = 0$

where $\delta$ is the Dirac delta function. If I solve the IVP using the Laplace transform, I get $y(t) = \frac{1}{3} e^{-t} \sin 3 t $. However, this function does not satisfy the initial conditions, as $y'(0) = 1$.

How would you interpret this result?