Question

Consider the following initial value problem: [ x'' + 36x = egin{cases} 9, & 0 leq t leq 5 \ 0, & t > 5 end{cases} , quad x(0) = 6, quad x'(0) = 0. ] Solve for the Laplace transform of $x(t)$ $X(s) = mathcal{L}{x(t)} =$

          Consider the following initial value problem:
[
x'' + 36x = egin{cases} 9, & 0 leq t leq 5 \ 0, & t > 5 end{cases} , quad x(0) = 6, quad x'(0) = 0. 
]
Solve for the Laplace transform of $x(t)$
$X(s) = mathcal{L}{x(t)} =$

Added by Stacy J.

A First Course in Differential Equations with Modeling Applications

Dennis G. Zill 11th Edition

Chapter 7

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11/21/2023

Step 1

Using the property that the Laplace transform of a derivative is s times the Laplace transform of the function minus the initial value of the function, we get: \[ s^2X(s) - s*x(0) - x'(0) + 36X(s) = \frac{9}{s}e^{-5s} \] Substituting the initial conditions x(0) Show more…

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