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Find the general solution of the differential equation. y" – 16y" + 68y' – 80y = 0. NOTE: Use c1, C2, and c3 for the arbitrary constants. y(t):

Find the general solution of the differential equation. y" – 16y" + 68y' – 80y = 0. NOTE: Use c1, C2, and c3 for the arbitrary constants. y(t):

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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Find the general solution of the differential equation. y" – 16y" + 68y' – 80y = 0. NOTE: Use C1, C2, and c3 for the arbitrary constants. y(t) =
Transcribed Image Text:Find the general solution of the differential equation. y" – 16y" + 68y' – 80y = 0. NOTE: Use C1, C2, and c3 for the arbitrary constants. y(t) =
Expert Solution
Step 1

Given differential equation is y'''−16y''+68y'−80y=0

We have to find the general solution of the given differential equation.

Write the auxiliary equation, which is given below

m3−16m2+68m−80=0

Now, solve m3−16m2+68m−80=0

⇒m−2m−4m−10=0⇒m−2=0 or m−4=0 or m−10=0⇒m=2 or m=4 or m=10

Hence, m=2, m=4 and m=10.

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