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Consider the following initial value problem: Edit y" + 4y' + 20y = d(t – 1); y(0) = 1, y'(0) = 0 a) Find the solution y(t). NOTE: Denote the Heaviside function by Uc(t) where ue(t) = 1 if t >c and 0 otherwise. Indicate separately the value of c. y(t) = U(t) e 26¬) sin(4 t – 1) + e¯ª cos(4 t) where c = T

Consider the following initial value problem: Edit y" + 4y' + 20y = d(t – 1); y(0) = 1, y'(0) = 0 a) Find the solution y(t). NOTE: Denote the Heaviside function by Uc(t) where ue(t) = 1 if t >c and 0 otherwise. Indicate separately the value of c. y(t) = U(t) e 26¬) sin(4 t – 1) + e¯ª cos(4 t) where c = T

Advanced Engineering Mathematics
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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Consider the following initial value problem: Edit y" + 4y' + 20y = 8(t – a); y(0) = 1, y'(0) =0 a) Find the solution y(t). NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 ift > c and 0 otherwise. Indicate separately the value of c. y(t) 1 Uelt) e 20^) sin(4 t - 7) + e™" cos(4 t) 4 where c = T b) Use a graphing utility to plot the solution y(t).
Transcribed Image Text:Consider the following initial value problem: Edit y" + 4y' + 20y = 8(t – a); y(0) = 1, y'(0) =0 a) Find the solution y(t). NOTE: Denote the Heaviside function by ue(t) where ue(t) = 1 ift > c and 0 otherwise. Indicate separately the value of c. y(t) 1 Uelt) e 20^) sin(4 t - 7) + e™" cos(4 t) 4 where c = T b) Use a graphing utility to plot the solution y(t).
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