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9. Suppose that z(t) = x (t) +iy(t) is a solution of z" + pz' + qz = Ae'o". (5.31) Substitute z(t) into equation (5.31). Then compare the real and imaginary parts of each side of the resulting equation to prove two facts: + px' + qx = A cos wt, у" + ру' + qу 3D A sin ot. = A sin wt. Write a short paragraph summarizing the significance of this result.

9. Suppose that z(t) = x (t) +iy(t) is a solution of z" + pz' + qz = Ae'o". (5.31) Substitute z(t) into equation (5.31). Then compare the real and imaginary parts of each side of the resulting equation to prove two facts: + px' + qx = A cos wt, у" + ру' + qу 3D A sin ot. = A sin wt. Write a short paragraph summarizing the significance of this result.

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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9. Suppose that z(t) = x(t) + iy(t) is a solution of z" + pz' + qz = Ae'o". (5.31) Substitute z (t) into equation (5.31). Then compare the real and imaginary parts of each side of the resulting equation to prove two facts: x" + px' + qx = A cos wt, y" + py' + qy A sin wt . Write a short paragraph summarizing the significance of this result.
Transcribed Image Text:9. Suppose that z(t) = x(t) + iy(t) is a solution of z" + pz' + qz = Ae'o". (5.31) Substitute z (t) into equation (5.31). Then compare the real and imaginary parts of each side of the resulting equation to prove two facts: x" + px' + qx = A cos wt, y" + py' + qy A sin wt . Write a short paragraph summarizing the significance of this result.
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