Show that the boundary conditions X(b)=wX(a) +zX'(a)

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SUMMARY

The discussion centers on proving the symmetry of the boundary conditions X(b) = wX(a) + zX'(a) and X'(b) = yX(a) + dX'(a) on the interval a ≤ x ≤ b, specifically under the condition that wd - zy = 1. A participant highlights that boundary conditions are symmetric if the expression f '(x)g(x) - f(x)g'(x) equals zero when evaluated at both endpoints. The confusion arises regarding the definitions of f(x) and g(x) in this context, as well as the implications of symmetry in boundary conditions.

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matpo39
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I need a little help getting started here,

Show that the boundary conditions X(b)=wX(a) +zX'(a)

and
X'(b) = yX(a) + dX'(a) on the interval a<=x<=b are symmetric if and only if wd-zy=1

i know that the a set of boundries are symmetric if f '(x)g(x) - f(x)g'(x) = 0 evaluated at x=a and x=b. but i am confused on what f(x) and g(x) would be.
if some one can help me get this problem started it would be greatly appreciated.

thanks
 
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What would it mean for the BC to be 'symmetric'?

X(a) = X(b) and X'(a) = -X'(b) perhaps.
 

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