Toronto Math Forum
APM3462016F => APM346Lectures => Chapter 4 => Topic started by: Shaghayegh A on November 14, 2016, 02:09:32 PM

http://www.math.toronto.edu/courses/apm346h1/20169/PDEtextbook/Chapter4/S4.2.P.html#mjxeqna
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 $y=xl/2=xL$. 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

Different eigenvalues. For the same eigenvalue it will be plain wrong