# Euler's Identity and Boundary Problems

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Consider the boundary value problem:

y" - 2y' + (1 + Î»)y = 0, y(0) = 0, y'(1) = 0

For which values of Î» does the problem have a non-trivial solution?

https://brainmass.com/math/fourier-analysis/eulers-identity-boundary-problems-414635

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The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

The equation is:

(1.1)

With the boundary conditions:

The equation is second order homogenous with constant coefficients. We "guess" as solution in the form:

(1.2)

Plugging this back into equation (1.1) we get the ...

#### Solution Summary

Euler's identity is carefully applied.

$2.49