y(0) = 1, y'(0) = −2 y" + 8y = 0 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 Now solve for Y(s) = A B and write the above answer in its partial fraction decomposition, Y(s): + Y(s) = s+a s+b Now by inverting the transform, find y(t) = + where a < b

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

Use the Laplace transform to solve the following initial value problem: 

y" + 8y' = 0_______y(0) = 1, y′(0) = -2
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
Now solve for Y(s)
and write the above answer in its partial fraction decomposition, y(s)
Y(s) =
=
Now by inverting the transform, find y(t)
=
+
=
A
s+a
+
B
s+b
where a < b
Transcribed Image Text:y" + 8y' = 0_______y(0) = 1, y′(0) = -2 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 Now solve for Y(s) and write the above answer in its partial fraction decomposition, y(s) Y(s) = = Now by inverting the transform, find y(t) = + = A s+a + B s+b where a < b
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