Question

Use the Laplace transform to solve the initial value problem $$y''-7y'+12y = f(t), y(0) = 0, y'(0) = 0$$ where $$f(t) = \begin{cases} 0 & \text{if } 0 \le t < 3 \\ -6t + \frac{37}{2} & \text{if } t \ge 3 \end{cases}$$ Note: Use u for the step function. y(t) =

Name: use the laplace transform to solve the initial value problem y 7y12y ft y0 0 y0 0 where ft begincases 0 textif 0 le t 3 6t frac372 textif t ge 3 endcases note use u for the step function yt 01225
Uploaded: 2020-06-23T13:42:43-08:00
Duration: 2 min 9 s
Channel: Sajin Shajee
Description: use the laplace transform to solve the initial value problem y 7y12y ft y0 0 y0 0 where ft begincases 0 textif 0 le t 3 6t frac372 textif t ge 3 endcases note use u for the step function yt 01225

          Use the Laplace transform to solve the initial value problem
$$y''-7y'+12y = f(t), y(0) = 0, y'(0) = 0$$
where
$$f(t) = \begin{cases}
0 & \text{if } 0 \le t < 3 \\
-6t + \frac{37}{2} & \text{if } t \ge 3
\end{cases}$$
Note: Use u for the step function.
y(t) =

$use the laplace transform to solve the initial value problem y 7y12y ft y0 0 y0 0 where ft begincases 0 textif 0 le t 3 6t frac372 textif t ge 3 endcases note use u for the step function yt 01225$

Added by Shawn P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sajin Shajee

06/23/2020

Step 1

$$L[y''-7y'+12y] = L[f(t)]$$ $$s^2Y(s) - sy(0) - y'(0) - 7(sY(s) - y(0)) + 12Y(s) = F(s)$$ Show more…

Show all steps

Thanks for your feedback!

Use the Laplace transform to solve the initial value problem $$y''-7y'+12y = f(t), y(0) = 0, y'(0) = 0$$ where $$f(t) = \begin{cases} 0 & \text{if } 0 \le t < 3 \\ -6t + \frac{37}{2} & \text{if } t \ge 3 \end{cases}$$ Note: Use u for the step function. y(t) =