# [R] Solution to differential equation

Mike Marchywka marchywka at hotmail.com
Wed Dec 15 18:26:44 CET 2010

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> Date: Wed, 15 Dec 2010 11:46:40 -0500
> From: msamtani at gmail.com
> To: r-help at r-project.org
> Subject: [R] Solution to differential equation
>
> Hello,
> I am trying to find the analytical solution to this differential equation
>
> dR/dt = k1*(R^k2)*(1-(R/Rmax)); R(0) = Ro
>
> k1 and k2 are parameters that need to fitted, while Ro and Rmax are the
> baseline and max value (which can be fitted or fixed). The response (R)
> increases
> initially at an exponential rate governed by the rate constants k1 and k2.
> Response has a S-shaped curve as a function of time and it approaches the
> value of Rmax at time approaches infinity.
>
> If there is an analytial solution to this differential equation then it

http://integrals.wolfram.com/index.jsp?expr=1%2F%28%28x^k2%29*%281-x%2Fkz%29%29&random=false

Not that its relevant but, since someone accused you of doing homework anyway,
I would like to state for the record that " a dog ate my Gradstein and Rhysik
Integral tables". And I would ask if anyone has one they want to get
rid of. I think some of these things you can ask for their strategies
not sure if Mathematica has a console dump of that type.

> makes my life easier when trying to perform some non-linear regression.
> Kindly provide the integration process so I can learn how to do it myself
> for future reference. I believe that the way would be
> to use integration by parts (I tried hard to find the solution but keep
> getting stuck).
>
> Mahesh
>
> [[alternative HTML version deleted]]
>
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