How Do You Rescale the Dimensionless Riccati Equation?

[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.

 

[Tide]

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

 

[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.

 

[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.