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For the differential equation    the boundary conditions are  
(i)  y = 0 for x = 0, and 
(ii) y = 0 for x = a   
The form of non-zero solutions of y (where m varies over all integers) are 
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
For the differential equation the boundary conditions are (i) y = 0 f...
Here y = c1 coskx + c2 sinkx ........... (1) be the solution of the given differential equation.
Now use boundary conditions
For x = 0, y = 0 gives c1 = 0. Equation − (1) becomes
y = c2 sin kx  .....(2)
For x = a, y = 0 given
For x = a, y = 0 given, c2 sinka = O. If c2 = 0 then (2) becomes y = 0, so it gives trival solution.
So take sin ka = 0
⇒ sin ka = sin nπ, η = 0,1,2,  
⇒ ka = nπ

be the solution, n 0,1,2,3.......
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For the differential equation the boundary conditions are (i) y = 0 for x = 0, and(ii) y = 0 for x = a The form of non-zero solutions of y (where m varies over all integers) area)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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