# Differential eqtn (What's wrong with my calculation?)

1. Jul 2, 2011

### athrun200

I would like to ask why I obtain a different answer from the book?
If I am wrong, how to obtain the correct answer?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Jul 2, 2011

### vela

Staff Emeritus
Rewrite the differential equation slightly to get
$$\rho^2u''(\rho)-l(l+1)u(\rho) = 0$$
Then substitute a trial solution of the form $\rho^r$ and then solve for r.

3. Jul 2, 2011

### athrun200

Is it another way to solve ODE?
What is the name of this method?

I can only remember to sub e^r:tongue2:

4. Jul 2, 2011

### vela

Staff Emeritus
5. Jul 2, 2011

### HallsofIvy

You basic error is trying to apply a method that works for equations with constant coeficients to an equation with variable coefficients. As a result your characteristic equation, which should not involve the idependent variable, is wrong and everything after that is wrong.

6. Jul 2, 2011

### athrun200

How to solve it?

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7. Jul 2, 2011