ODEs don't get much easier than this... integration by parts is overkill. See the posting guide re homework.
"mahesh samtani" <msamt...@gmail.com> wrote: >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 >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]] > >______________________________________________ >R-help@r-project.org mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide >http://www.R-project.org/posting-guide.html >and provide commented, minimal, self-contained, reproducible code. --------------------------------------------------------------------------- Jeff Newmiller The ..... ..... Go Live... DCN:<jdnew...@dcn.davis.ca.us> Basics: ##.#. ##.#. Live Go... Live: OO#.. Dead: OO#.. Playing Research Engineer (Solar/Batteries O.O#. #.O#. with /Software/Embedded Controllers) .OO#. .OO#. rocks...1k --------------------------------------------------------------------------- Sent from my phone. Please excuse my brevity. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
