Explore BrainMass
Share

Euler's Identity and Boundary Problems

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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?

© BrainMass Inc. brainmass.com March 21, 2019, 10:22 pm ad1c9bdddf
https://brainmass.com/math/fourier-analysis/eulers-identity-boundary-problems-414635

Solution Preview

Hello and thank you for posting your question to Brainmass!

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.

$2.19