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. 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
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 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.
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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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.
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.
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