ShowerHead
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Homework Statement
I have to find the eigenvalues&function of the eqn:
y''+\lambda y =0
With the boundary conditions:
y(0)+y'(0) = 0 and y(\pi) =0
Homework Equations
The Attempt at a Solution
I get the general equations, okay, but am having trouble due to the boundary conditions.
Assuming \lambda>0, then get the general solution:
y(x)=A\sin(x\sqrt{\lambda})+B\cos(x\sqrt{\lambda})
The best i can do now is that:
y(\pi)=A\sin(\sqrt{\lambda}\pi)+B\cos(\sqrt{\lambda}\pi)=0
Which can only be valid if B = 0 and \sqrt{\lambda} = n where n is a positive integer.
Now I run into problems, the second bc gives:
y(0)=A\sin(n 0)=0
y'(0)=nA\cos( n 0)=nA
So:
y(0)+y'(0) = 0 + nA = 0
Am I on the right track, or can anyone see where I am messing up?
Thanks.