d³y_d²y_dy dx³ dx² dx -+y=0 HINT: substitu

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 35RE
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Differential Equations

Please, show all the work and every step

(5)
d'y d'y dy
dx³ dx²
+ y = 0
dx
HINT: substitute y = Aerx to find roots of characteristic equations by inspection
ri=1; use long division or inspection to find other roots and r2=1 and r3 = -1; One
of the roots are repeated.
ANSWER: y = Aex+Bxex+Ce-x
Transcribed Image Text:(5) d'y d'y dy dx³ dx² + y = 0 dx HINT: substitute y = Aerx to find roots of characteristic equations by inspection ri=1; use long division or inspection to find other roots and r2=1 and r3 = -1; One of the roots are repeated. ANSWER: y = Aex+Bxex+Ce-x
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