Consider the following initial value problem. y" + 8y' + 25y = 8(t – n) + 8(t – 7x), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7ts -TS + e + (s + 8) (s + 4)2 + 32 e L{y} = Use the Laplace transform to solve the given initial-value problem. A(a-)sin 3(t – 1) x )· «(t - «) + ( \ e-^'cos(3t) × )- a( - 4 -4t 'e sin (3t) | × 3 y(t) = t - n) + 3 7n
Consider the following initial value problem. y" + 8y' + 25y = 8(t – n) + 8(t – 7x), y(0) = 1, y'(0) = 0 Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7ts -TS + e + (s + 8) (s + 4)2 + 32 e L{y} = Use the Laplace transform to solve the given initial-value problem. A(a-)sin 3(t – 1) x )· «(t - «) + ( \ e-^'cos(3t) × )- a( - 4 -4t 'e sin (3t) | × 3 y(t) = t - n) + 3 7n
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:Consider the following initial value problem.
у" + 8y' + 25у %3D 6(t — л) + 6(t — 7л), у(0) %3D 1, у'(0)
= 0
-
Find the Laplace transform of the differential equation. (Write your answer as a function of s.)
-TS
-7Ts
+ e
+ (s + 8)
e
L{y}
(s + 4)² + 32
Use the Laplace transform to solve the given initial-value problem.
4 -4t
H )+( že
1,-4(1-1)sin 3(t– n) | ×
). a(e - -) + ( e Hcos(3t) ×
'e sin( 3t) x
-4t.
y(t)
t - T
t -
3
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