# [R] Solution to differential equation

Jeff Newmiller jdnewmil at dcn.davis.ca.us
Wed Dec 15 18:00:41 CET 2010

```ODEs don't get much easier than this... integration by parts is overkill.

See the posting guide re homework.

"mahesh samtani" <msamtani at 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).
>
>Mahesh
>
>	[[alternative HTML version deleted]]
>
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>and provide commented, minimal, self-contained, reproducible code.

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