When solving a differential equation using the Laplace transform, you apply the Laplace transform to both sides of the equation and then solve for Y(s) before applying the inverse Laplace transform. Find Y (s) for the initial value problem y" – 5y' + 6y = h(t – 1) with y(0) = 1 and y'(0) = 0. s+5 O Y = e (s-3)(s-2) (s-3)(8–2) s+1 O Y = - s(s-3)(s-2) (s-3)(s-2) e (s-1) (8-1)(s-3)(s-2) 8-5 Y = + (s-3)(s-2) 1 OY e s(s–3)(s–2) + (s-3)(8-2) O Y = + (8-3)(s-2) 8-5 s(8-3)(s-2)
When solving a differential equation using the Laplace transform, you apply the Laplace transform to both sides of the equation and then solve for Y(s) before applying the inverse Laplace transform. Find Y (s) for the initial value problem y" – 5y' + 6y = h(t – 1) with y(0) = 1 and y'(0) = 0. s+5 O Y = e (s-3)(s-2) (s-3)(8–2) s+1 O Y = - s(s-3)(s-2) (s-3)(s-2) e (s-1) (8-1)(s-3)(s-2) 8-5 Y = + (s-3)(s-2) 1 OY e s(s–3)(s–2) + (s-3)(8-2) O Y = + (8-3)(s-2) 8-5 s(8-3)(s-2)
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:When solving a differential equation using the Laplace transform, you apply
the Laplace transform to both sides of the equation and then solve for Y(s)
before applying the inverse Laplace transform.
Find Y (s) for the initial value problem y" – 5y' + 6y = h(t – 1) with
y(0) = 1 and y'(0) = 0.
s+5
O Y =
e
(s-3)(s-2)
(s-3)(8–2)
s+1
O Y = -
s(s-3)(s-2)
(s-3)(s-2)
e (s-1)
(8-1)(s-3)(s-2)
8-5
Y =
+
(s-3)(s-2)
1
OY
e
s(s–3)(s–2)
+
(s-3)(8-2)
O Y =
+
(8-3)(s-2)
8-5
s(8-3)(s-2)
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