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Consider the following initial value problem. y" + 8y' + 25y = 8(t – x) + 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.) -TS e -7as + (s + 8) +e L{y} = (s+4)² + 3² Use the Laplace transform to solve the given initial-value problem. 4-4'e sin (31) x 1 -4(n-t) 2. 3 'sin 3(1 – a) × ) · a(e – a) + (| 4t e-"cos(3t) x y(t) = t- · Ut -| 77

Consider the following initial value problem. y" + 8y' + 25y = 8(t – x) + 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.) -TS e -7as + (s + 8) +e L{y} = (s+4)² + 3² Use the Laplace transform to solve the given initial-value problem. 4-4'e sin (31) x 1 -4(n-t) 2. 3 'sin 3(1 – a) × ) · a(e – a) + (| 4t e-"cos(3t) x y(t) = t- · Ut -| 77

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. у" + 8y' + 25у %3D 6(t — л) + 6(t — 7л), у(0) %3D 1, у'(0) %3D 0 - Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7ts -TTS +e + (s + 8) e L{y} = (s + 4)2 + 32 Use the Laplace transform to solve the given initial-value problem. Y(t) = (| 4-4'e sin (31) x )+( že 'e sin (3t) x 1,-4(π-t), -4(x-1) sin 3(t – 1) × )· u(t - =) + ( e"cos(3t) x -4'cos(3t) * COS t - 3 Need Help? Read It
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) %3D 0 - Find the Laplace transform of the differential equation. (Write your answer as a function of s.) -7ts -TTS +e + (s + 8) e L{y} = (s + 4)2 + 32 Use the Laplace transform to solve the given initial-value problem. Y(t) = (| 4-4'e sin (31) x )+( že 'e sin (3t) x 1,-4(π-t), -4(x-1) sin 3(t – 1) × )· u(t - =) + ( e"cos(3t) x -4'cos(3t) * COS t - 3 Need Help? Read It
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