# Define a solution the given initial-value problem. 4'' + 4y'4y=delta(t - 4) y(0) = 1 y'(0) = 2

Define a solution the given initial-value problem.

$y\left(0\right)=1$
${y}^{\prime }\left(0\right)=2$
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To solve, we use the properties of the Laplace transform and the Laplace table
The Laplace transform satisfies the linearity properties

$L\left[cf\right]=cL\left[f\right]$
For all transfotmable functions f and g and constants c.

Substitute initial conditions,
$y\left(0\right)=1$
${y}^{\prime }\left(0\right)=2$
Solve for $Y\left(s\right).$

Inverse transform: