# Find the value of n

1. Sep 18, 2014

### utkarshakash

1. The problem statement, all variables and given/known data
Find the value of n so that the equation $V=r^n(3 \cos ^3 \theta -1)$ satisfies the relation
$$\dfrac{\partial}{\partial r} \left( r^2 \dfrac{\partial V}{\partial r} \right) + \dfrac{1}{\sin \theta}\dfrac{\partial}{\partial \theta} \left( \sin \theta \dfrac{\partial V}{\partial \theta} \right)=0$$

2. Relevant equations

3. The attempt at a solution
The final equation after differentiation comes out to be
$$n(n+1)(3 \cos ^3 \theta -1) = 18 \cos \theta (2\cos ^2 \theta -1)$$

What should I substitute for θ ?

2. Sep 18, 2014

### Simon Bridge

Why should you need to substitute something for theta?
Recheck your algebra... you final relation is saying there is no value of n that will make V satisfy the PDE.

3. Sep 18, 2014

### utkarshakash

I've already checked it thrice but couldn't find any error! Can you please show me where I'm going wrong?

4. Sep 18, 2014

### Ray Vickson

How can anybody tell where you went wrong? You have not shown your work in detail.

I (or Maple) get something completely different from your result.