# Anomalous differential equation

1. Jul 1, 2010

### chooxani

I am doing a physics fight and the problem ive got to solve is as follows:
Two magnets are arranged on top of each other such that one of them is fixed and the other one can move vertically. investigate the oscillation fo the magnet.

The equation is

my''-by'-((m_1*m_2)/(miu*4*pi*|y|^2))=0

or where k=-(m_1*m_2)/(miu*4*pi),

m*y'' - b*y' - k*|y|^2 = 0

2. Jul 2, 2010

### Eynstone

Put y'=p, y'' =p dp/dy. Rearranging, you get a Riccati equation in p and y.
Therefore, it would be unjust to insist on the exact solution. I suggest that we substitute z=y* exp(-bt/2m) and simplify the equation.We could either linearise tthe equation or use the perturbation methods.

3. Jul 4, 2010

### chooxani

thanks but where did z come from? also could u please write the 'solution' with the steps? bear with me but i need to understand this thing right.

4. Jul 4, 2010

### HallsofIvy

my"- by'- b|y|^2= 0 is not at all like the first equation you wrote:
my''-by'-((m_1*m_2)/(miu*4*pi*|y|^2))=0.

One has the |y|^2 in the numerator and the other in the denominator. By the way, as long as y is a real number, |y|^2= y^2 so you don't need the "| |".

As for "where did z come from", Eynestone just gave it to you. He is defining z to be y* exp(-bt/2m) in hopes that this substitution will simplify the equation.

5. Jul 4, 2010

### manlyman62

I'm sorry, I have little to contribute in terms of solving the DE, but I must ask: what is a physics fight?