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List the values for L such that the function y = sin (Lx) is a nontrivial solution for the ODE 25y + y = 0. O 5,-5 5,0 O 5,1 O 0 O 5,0,-5 0,-5

List the values for L such that the function y = sin (Lx) is a nontrivial solution for the ODE 25y + y = 0. O 5,-5 5,0 O 5,1 O 0 O 5,0,-5 0,-5

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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List the values for L such that the function y = 25y + y = 0. O 5,-5 5,0 O 5,1 0 5,0,-5 0,-5 sin (Lx) is a nontrivial solution for the ODE
Transcribed Image Text:List the values for L such that the function y = 25y + y = 0. O 5,-5 5,0 O 5,1 0 5,0,-5 0,-5 sin (Lx) is a nontrivial solution for the ODE
Expert Solution
Step 1: ''Introduction to the solution''

The  given equation  is   open parentheses 25 y plus y apostrophe apostrophe close parentheses equals 0

                             that  is, open parentheses y apostrophe apostrophe plus 25 y close parentheses equals 0............ left parenthesis 1 right parenthesis

It  is  given that y equals sin left parenthesis L x right parenthesis space is a  solution  of the  given differential  equation(1).

We  have  to  find  the  values  of  L for  which  y equals sin left parenthesis L x right parenthesis  is  a  solution of  the  given differential  equation(1).

Since,  we  want non-trivial solution  of the  given differential  equation, it follows  that y not equal to 0 for  any values  of L.


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