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Euler's Identity and Boundary Problems

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Consider the boundary value problem:
y" - 2y' + (1 + λ)y = 0, y(0) = 0, y'(1) = 0
For which values of λ does the problem have a non-trivial solution?

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The equation is:
With the boundary conditions:

The equation is second order homogenous with constant coefficients. We "guess" as solution in the form:
Plugging this back into equation (1.1) we get the ...

Solution Summary

Euler's identity is carefully applied.