I've been going round in circles with this problem for days:(adsbygoogle = window.adsbygoogle || []).push({});

Find the eigenvalues and associated normalised eigenfunctions of the operator L:

[tex]L_y = x^2 y'' + 2 xy' + \frac{y}{4}[/tex]

Boundary conditions [tex]y(1)=y(e)=0[/tex]

So what I've done:

substitute [tex]x = \exp(t)[/tex]

Then [tex]L_y = \frac{d^2y}{dt^2} + \frac{dy}{dt} + \frac{y}{4}[/tex] where the differentials are now y wrt t

The eigenvalue equation is [tex]L_y = X_n y[/tex] where [tex]X_n[/tex] are my eigenvalues

Then I solve [tex]y'' + y' + (1/4 - X_n)y = 0[/tex]

and get [tex]y = \exp (-1/2 t) (A \exp(+\sqrt(X_n)t) + B \exp(-\sqrt(X_n)t)[/tex]

Applying the boundary problems I find B = - A

and that [tex]X_n == 0[/tex]. Which doesn't seem right!

Am I on the right track here or have I missed the point totally!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Eigenfunction equation

**Physics Forums | Science Articles, Homework Help, Discussion**