Obtain the dimensionless ODE

1. Oct 16, 2005

fresh

Been working on this problem for an hour now.

Rescale

(dh/dt) = s - a*p*g*(h + (h^2)/R)

to obtain the dimensionless ODE

y' = a - y - y^2

It seems that the differential equation involving dh/dt is a ricatti equation and I tried finding a particular solution but have had no luck. Any help is welcomed.

Thanks.

2. Oct 16, 2005

Tide

Are you having difficulty obtaining the dimensionless equation or in solving it? In either case, what have you done so far?

3. Oct 16, 2005

fresh

I am having difficulty with the dimensionless part. I am really not sure what to do. I would think that you would need to make a substitution but i am not sure what. I just need a push in the right direction since I want to solve it myself.

4. Oct 16, 2005

Tide

There are several ways to approach it. Here's one: Let h = Ay and t = Bx with constants A and B. y and x will be your new variables. Substitute into the DE then choose A and B to put the new DE into the required form.