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Obtain the dimensionless ODE

  1. Oct 16, 2005 #1
    Been working on this problem for an hour now.


    (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.

  2. jcsd
  3. Oct 16, 2005 #2


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    Are you having difficulty obtaining the dimensionless equation or in solving it? In either case, what have you done so far?
  4. Oct 16, 2005 #3
    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.
  5. Oct 16, 2005 #4


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    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.
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