Solve the given initial value problem using the method of Laplace transforms.
$$
y'' + 2y' + 10y = g(t), y(0) = -1, y'(0) = 0, \text{ where } g(t) = \begin{cases} 10, & 0 \le t \le 13, \\ 20, & 13 < t < 26, \\ 0, & 26 < t \end{cases}
$$
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The solution has the form $$y(t) = p(t) + q(t)u(t - \alpha) + r(t)u(t-\beta)$$, where u(t) is the unit step function. Let $$\alpha < \beta$$. Identify the values of $$\alpha$$ and $$\beta$$
$$\alpha = 13$$
$$\beta = 26$$
(Simplify your answers.)
Identify p(t).
p(t) =
(Use parentheses to clearly denote the argument of each function.)
