Question

(25 points) Use the Laplace transform to solve the following initial value problem: $y'' + 6y' = 0$ $y(0) = 6, y'(0) = 1$ First, using $Y$ for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L}\{y(t)\}$, find the equation you get by taking the Laplace transform of the differential equation Now solve for $Y(s) = $ 0 and write the above answer in its partial fraction decomposition, $Y(s) = $ $Y(s) = $ +$ Now by inverting the transform, find $y(t) = $ $\frac{A}{s+a} + \frac{B}{s+b}$ where $a < b

          (25 points) Use the Laplace transform to solve the following initial value problem:
$y'' + 6y' = 0$
$y(0) = 6, y'(0) = 1$
First, using $Y$ for the Laplace transform of $y(t)$, i.e., $Y = \mathcal{L}\{y(t)\}$,
find the equation you get by taking the Laplace transform of the differential equation
Now solve for $Y(s) = $
0
and write the above answer in its partial fraction decomposition, $Y(s) = $
$Y(s) = $
+$
Now by inverting the transform, find $y(t) = $
$\frac{A}{s+a} + \frac{B}{s+b}$ where $a < b

$(25 points) Use the Laplace transform to solve the following initial value problem: y” + 6y' = 0 y(0) = 6, y'(0) = 1 First, using Y for the Laplace transform of y(t), i.e., Y = ℒ{y(t)}, find the equation you get by taking the Laplace transform of the differential equation Now solve for Y(s) = 0 and write the above answer in its partial fraction decomposition, Y(s) = Y(s) = +Now by inverting the transform, findy(t) = (A)/(s+a) + (B)/(s+b)wherea < b$

Added by Rosario A.

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