Transform the differential equation 9y" +14-81 - 126y= 5et y(0) = 0 3/(0) = 0 3'(0) = 1 into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). 0-0 Therefore Y - 8+1 Taking the inverse Laplace transform we get

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.8: Applications Of Vector Spaces
Problem 39E
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Transform the differential equation
into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)).
0-0
Therefore
Y
-
+3
8+1
9y" + 14"-81y - 126y=5e-t
y(0) = 0
/(0) = 0
y" (0) = 1
Taking the inverse Laplace transform we get
Transcribed Image Text:Transform the differential equation into an algebraic equation by taking the Laplace transform of each side. Use Y for the Laplace transform of y, (not Y(s)). 0-0 Therefore Y - +3 8+1 9y" + 14"-81y - 126y=5e-t y(0) = 0 /(0) = 0 y" (0) = 1 Taking the inverse Laplace transform we get
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