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Show that if the pair of complex-valued functions Y = f,(1) + if,(1) ュ=g()+ig.() (where f, f2, g, and g, are all real-valued functions) is a solution to the above system, then the real parts y, = f(t), y2 = g,(1) and the imaginary parts y = f2(t), y, = g,(1) are both solutions.

Show that if the pair of complex-valued functions Y = f,(1) + if,(1) ュ=g()+ig.() (where f, f2, g, and g, are all real-valued functions) is a solution to the above system, then the real parts y, = f(t), y2 = g,(1) and the imaginary parts y = f2(t), y, = g,(1) are both solutions.

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 a normal, homogeneous, constant coefficient system of differential equations: yi = ay1 +A12Y2 +
Transcribed Image Text:Consider a normal, homogeneous, constant coefficient system of differential equations: yi = ay1 +A12Y2 +
Show that if the pair of complex-valued functions y, = f,(t)+ if,(t) Y2 = g,(t) +ig,(t) (where f, f,, g, and g, are all real-valued functions) is a solution to the above system, then the real parts y = f,(1), y2 = g1(t) and the imaginary parts y = f,(t), y, = g2(t) are both solutions.
Transcribed Image Text:Show that if the pair of complex-valued functions y, = f,(t)+ if,(t) Y2 = g,(t) +ig,(t) (where f, f,, g, and g, are all real-valued functions) is a solution to the above system, then the real parts y = f,(1), y2 = g1(t) and the imaginary parts y = f,(t), y, = g2(t) are both solutions.
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