Use the Laplace transform to solve the following initial value problem: + 2y + ly=0 y(0)=-7, 1/(0)=-4 a. 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 2=0 b. Solve for Y(s) = c. write the above answer in its partial fraction decomposition, Y(s) + + (+) Y(*)-0-0 d. Now, by inverting the transform, find 3(0) =
Use the Laplace transform to solve the following initial value problem: + 2y + ly=0 y(0)=-7, 1/(0)=-4 a. 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 2=0 b. Solve for Y(s) = c. write the above answer in its partial fraction decomposition, Y(s) + + (+) Y(*)-0-0 d. Now, by inverting the transform, find 3(0) =
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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Transcribed Image Text:Use the Laplace transform to solve the following initial value problem:
+2y + 1y=0
v(0)-7, 1/(0)=-4
a. Using Y for the Laplace transform of y(t), i.e., Y =C{y(t)), find the equation you get by taking the Laplace transform of the differential
equation
2=0
b. Solve for
Y(s) =
c. write the above answer in its partial fraction decomposition, Y(s) + (+)
Y()-0-0
d. Now, by inverting the transform, find
y(t) =
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