# [SOLVED]Laplace equation polar where does the ln constant come from

#### dwsmith

##### Well-known member
So we have the two ODE solutions are the cosine/sine and $r^n$ since it was a Cauchy Euler type.
For the steady state, the solution is just a constant since it has to have period 2pi. But with $r^n$, how with lambda equal to zero does $\ln r$ come into play?

If my question is hard to follow, go here http://web.mit.edu/6.013_book/www/chapter5/5.7.html

Look at (9) and you will see ln r. I don't see we get that.

Last edited:

#### Sudharaka

##### Well-known member
MHB Math Helper
So we have the two ODE solutions are the cosine/sine and $r^n$ since it was a Cauchy Euler type.
For the steady state, the solution is just a constant since it has to have period 2pi. But with $r^n$, how with lambda equal to zero does $\ln r$ come into play?

If my question is hard to follow, go here http://web.mit.edu/6.013_book/www/chapter5/5.7.html

Look at (9) and you will see ln r. I don't see we get that.
Note that when $$m=0$$ we have,

$r\frac{d}{dr}\left(\frac{1}{r}\frac{dR}{dr}\right)=0$

Now try to find $$R$$.