- Thread starter
- #1

\[

f(x) = \lambda\int_0^1xy^2f(y)dy

\]

I am trying to determine the eigenvalues and eigenfunction. I know that the \(\frac{1}{\lambda}\) are the eigenvalues.

We can write \(f(x) = xA\) and \(A = \lambda\int_0^1y^2f(y)dy\).

\[

A\Bigg(1 - \lambda\int_0^1y^3dy\Bigg) = 0\quad (*)

\]

So is the eigenvalue only one value which would be what I get when I solve for 1 over lambda?

\[

\frac{1}{\lambda} = \frac{1}{4}

\]

Is \((*)\) the eigenfunction? If not, how do I find the eigenfunction?