Prove that the eigenfunctions corresponding to different eigenvalues (of the following

Chapter 5, Problem 5.5.2

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Prove that the eigenfunctions corresponding to different eigenvalues (of the following eigenvalue problem) are orthogonal:

\(\frac{d}{d x}\left[p(x) \frac{d \phi}{d x}\right]+q(x) \phi+\lambda \sigma(x) \phi=0\)

with the boundary conditions

\(\begin{aligned}
\phi(1) & =0 \\
\phi(2)-2 \frac{d \phi}{d x}(2) & =0 .
\end{aligned}\)

What is the weighting function?

Questions & Answers

QUESTION:

Prove that the eigenfunctions corresponding to different eigenvalues (of the following eigenvalue problem) are orthogonal:

\(\frac{d}{d x}\left[p(x) \frac{d \phi}{d x}\right]+q(x) \phi+\lambda \sigma(x) \phi=0\)

with the boundary conditions

\(\begin{aligned}
\phi(1) & =0 \\
\phi(2)-2 \frac{d \phi}{d x}(2) & =0 .
\end{aligned}\)

What is the weighting function?

ANSWER:

Step 1 of 3

Let \(\phi_{1}\) and \(\phi_{2}\) be the eigenfunction of the Sturm-Liouville operator L corresponding to two different eigenvalues \(\lambda_{1}\) and \(\lambda_{2}\)

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back