/" – 6y + 18y =0 y(0) = 0, (0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = find the equation you get by taking the Laplace transform of the differential equation = L{y(t)}. = 0 3. Now solve for Y(s)= s2-6s + 18 By completing the square in the denominator and inverting the transform, find y(t) = et sin(3r)
/" – 6y + 18y =0 y(0) = 0, (0) = 3 First, using Y for the Laplace transform of y(t), i.e., Y = find the equation you get by taking the Laplace transform of the differential equation = L{y(t)}. = 0 3. Now solve for Y(s)= s2-6s + 18 By completing the square in the denominator and inverting the transform, find y(t) = et sin(3r)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use Laplace transform to solve the following:
Transcribed Image Text:y– 6y + 18y = 0
y(0) = 0, v(0) =
First, using Y for the Laplace transform of y(t), i.e. Y =
find the equation you get by taking the Laplace transform of the differential equation
= L{y(t)}.
= 0
3
Now solve for Y(s):
s2-6s + 18
By completing the
square
in the denominator and inverting the transform, find
y(t)
et sin (31)
Transcribed Image Text:+ 8y + 16y =0
y(0) = 6, (0) = -4
First, using Y for the Laplace transform of y(t), ie., Y =
find the equation you get by taking the Laplace transform of the differential equation
= L{y(t}.
= 0
Now solve for Y(s)
and write the above answer in its partial fraction decomposition, Y(s) =. +
(sta)
6.
Y(s) =
s+4
Now by inverting the transform, find y(t)
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