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cue928
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Homework Statement
y'' + (lambda)y = 0, y'(0) = 0, y(1) = 0
We are told that all eigenvalues are nonnegative.
Even with looking at the solution manual, I am unsure how to start setting these up. I've been starting by doing the following:
y(x) = A cos cx + B sin dx
y'(x) = -Ac sin(cx) + Bd cos(dx)
Subbing in the initial values:
y'(0)=0: 0 = B
This leaves y(x) = A cos (cx)
But this is also where I'm breaking down. I understand from y(1) = 0 that I am looking for a value of c such that the result is 0?
I mean, what should I be looking for on setting these up? That problem seems relatively straight forward but the next one I tried, y''+(lambda)y = 0, y(-pi) = 0, y(pi) = 0, has me baffled. Any guidance would be greatly appreciated.
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