renegade05
Full Member
- Joined
- Sep 10, 2010
- Messages
- 260
How would I solve this :
\(\displaystyle -(xu')'=\frac{1}{x} \ln{x} \enspace 1<x<e\)
\(\displaystyle u(1)=0 \enspace, u'(e)=0\)
I want to expand this with:
\(\displaystyle u(x) = \sum_{n=1} ^{\infty} b_n X_n(x)\)
Where \(\displaystyle X_n(x)\) are the eigenfunctions of a S-L problem.
\(\displaystyle b_n\) are some constants.
I want to express the solution as a single integral, from x = 1 to x = e.
Can someone please show me how to expand this? How can I find the eigenfunctions and the b_n. I know it is easy to solve with different methods - but I would like to do it this way to get a better grasp of similar problems. Thanks!
The lack of a lambda is really throwing me off - no idea how to do this.
\(\displaystyle -(xu')'=\frac{1}{x} \ln{x} \enspace 1<x<e\)
\(\displaystyle u(1)=0 \enspace, u'(e)=0\)
I want to expand this with:
\(\displaystyle u(x) = \sum_{n=1} ^{\infty} b_n X_n(x)\)
Where \(\displaystyle X_n(x)\) are the eigenfunctions of a S-L problem.
\(\displaystyle b_n\) are some constants.
I want to express the solution as a single integral, from x = 1 to x = e.
Can someone please show me how to expand this? How can I find the eigenfunctions and the b_n. I know it is easy to solve with different methods - but I would like to do it this way to get a better grasp of similar problems. Thanks!
The lack of a lambda is really throwing me off - no idea how to do this.
