a and d needs a solution

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a and d needs a solution

Use the Laplace transform to solve the following initial value problem:
y" + 7y - 18y=0
y(0) = 1, y'(0) = 1
a. 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
= 0
b. Now solve for
Y(s):
=
s+8
(S-2) (s+9)
=
c. Write the above answer in its partial fraction decomposition, Y(s) =
where a < b
Y(s) =
S
10
11
2
1
11
s +9
d. Now by inverting the transform, find
y(t) = .
A
B
+
s+a s+b
Transcribed Image Text:Use the Laplace transform to solve the following initial value problem: y" + 7y - 18y=0 y(0) = 1, y'(0) = 1 a. 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 = 0 b. Now solve for Y(s): = s+8 (S-2) (s+9) = c. Write the above answer in its partial fraction decomposition, Y(s) = where a < b Y(s) = S 10 11 2 1 11 s +9 d. Now by inverting the transform, find y(t) = . A B + s+a s+b
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