. Find the general solutions for the following linear, 2nd-order ODEs and de- scribe the behaviour. (a) (b) (c) (d) d²y dy +2- +6y=0, dx Y d²y 3- + = dr² 3 d²y dy dr² 16- 40- +25y = 0, dr d²y dy + dr2 dr - 6y=0. -
. Find the general solutions for the following linear, 2nd-order ODEs and de- scribe the behaviour. (a) (b) (c) (d) d²y dy +2- +6y=0, dx Y d²y 3- + = dr² 3 d²y dy dr² 16- 40- +25y = 0, dr d²y dy + dr2 dr - 6y=0. -
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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Question
Transcribed Image Text:. Find the general solutions for the following linear, 2nd-order ODEs and de-
scribe the behaviour.
(a)
(b)
(c)
(d)
d²y
d²y Y
dr²
3-
dy
+2-
dx
16-
+6y= 0,
+ =
3
d²y dy
dr²
40- +25y = 0,
dr
d²y dy
+
dr2 dr
- 6y=0.
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Transcribed Image Text:3. Apply the following conditions to the corresponding ODE solutions in Q2.
State whether or not the conditions make it an initial value problem or a
boundary value problem. Determine if solution is unique.
y(0) = 3, y'(0) = √5,
y(0) = 1, y(3π) = -1,
9
4'
(a)
(b)
(c)
(d)
y(0) = 3, y'(0)
y(0) = 0, y(1) = 1.
Solution
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