Solution to differential equation
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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). Please help, Mahesh [[alternative HTML version deleted]]
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