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(1) Consider the second-order equation y" + 2y' - 8y = f(t) with initial conditions y(0) = 1 and y′(0) = −10. (i) Solve this equation in terms of a convolution integral of f(t) (do not yet use the function from (2ii) below). (ii) Now apply the solution you found in (2i) to f(t) := 36e²t.

(1) Consider the second-order equation y" + 2y' - 8y = f(t) with initial conditions y(0) = 1 and y′(0) = −10. (i) Solve this equation in terms of a convolution integral of f(t) (do not yet use the function from (2ii) below). (ii) Now apply the solution you found in (2i) to f(t) := 36e²t.

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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(1) Consider the second-order equation y" + 2y' - 8y = f(t) with initial conditions y(0) 1 and y'(0) = -10. (i) Solve this equation in terms of a convolution integral of f(t) (do not yet use the function from (2ii) below). (ii) Now apply the solution you found in (2i) to f(t) := 36e²t. =
Transcribed Image Text:(1) Consider the second-order equation y" + 2y' - 8y = f(t) with initial conditions y(0) 1 and y'(0) = -10. (i) Solve this equation in terms of a convolution integral of f(t) (do not yet use the function from (2ii) below). (ii) Now apply the solution you found in (2i) to f(t) := 36e²t. =
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