# Toronto Math Forum

## APM346-2016F => APM346--Lectures => Chapter 4 => Topic started by: Shaghayegh A on November 14, 2016, 02:09:32 PM

Title: HA 6, problem 3c (sections 4.1 and 4.2)
Post by: Shaghayegh A on November 14, 2016, 02:09:32 PM
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter4/S4.2.P.html#mjx-eqn-a

For 3c: I assume that M(y) and N(y) are two arbitrary eigenfunctions with the same eigenvalues $\omega$. Then, M and N satisfy
$$Y^{(4)} (y)=\omega^4 Y(y) \\ Y(-L)=Y_y (-L)=0 \\ Y(L)=Y_y(L)=0$$ where I've switched coordinate systems so that $y=x-l/2=x-L$. I want to prove
$$\int_{-L}^{L} M(y) N(y) dy=0$$ but I'm not sure how to do that. Any advise?
Thank you
Title: Re: HA 6, problem 3c (sections 4.1 and 4.2)
Post by: Victor Ivrii on November 15, 2016, 07:01:18 AM
Different eigenvalues. For the same eigenvalue it will be plain wrong