# The given initial-value problem. y'' - 2y' - 8y = 5 y(0) = 1 y' (0) = 0

The given initial-value problem.

$y\left(0\right)=1$
${y}^{\prime }\left(0\right)=0$
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Margot Mill
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.
Laplace transform:

$\text{Undefined control sequence \8}$

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

Inverse transform: