Consider the following ODE: d'y + 16y=0 Now do the following: • Classify the ODE • Find all solutions to the ODE. Hint: Try guessing that y = er then solve for r. • Consider the set of all solutions to this ODE and find a set of solutions that spans it. That is, if S is the set of all solutions, find a finite number of solutions y₁, Y2, ..., Yn so that S = spank (y₁, Y2, ..., Yn). • All the solutions in S will be continuous functions on R. Is S a subspace of C (R)? Show why or why not?
Consider the following ODE: d'y + 16y=0 Now do the following: • Classify the ODE • Find all solutions to the ODE. Hint: Try guessing that y = er then solve for r. • Consider the set of all solutions to this ODE and find a set of solutions that spans it. That is, if S is the set of all solutions, find a finite number of solutions y₁, Y2, ..., Yn so that S = spank (y₁, Y2, ..., Yn). • All the solutions in S will be continuous functions on R. Is S a subspace of C (R)? Show why or why not?
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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Transcribed Image Text:Consider the following ODE:
d'y + 16y=0
dr²
Now do the following:
• Classify the ODE
• Find all solutions to the ODE. Hint: Try guessing that y=e" then solve for r.
• Consider the set of all solutions to this ODE and find a set of solutions that spans it. That is, if S is the set of all
solutions, find a finite number of solutions y₁, y2,..., Yn
• All the solutions in S will be continuous functions on R.
so that S = span (y₁, 92, ..., yn).
S a subspace of C
(R)? Show why or why not?
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