       Re: How to solve or approximate a first order differential equation ?

• To: mathgroup at smc.vnet.net
• Subject: [mg123224] Re: How to solve or approximate a first order differential equation ?
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Sun, 27 Nov 2011 04:13:56 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Clear[y];

data = {{1, 0.033}, {2, 0.054}, {5, 0.088}};

With[{C = 1/9},
Column[{
model = DSolve[
{y'[t] == -A (y[t])^2 + B (C - y[t]), y == 0},
y[t], t][],
param = FindFit[data, y[t] /. model, {A, B}, t],
Plot[y[t] /. model /. param, {t, 0, Max[data[[All, 1]]]},
ImageSize -> 400, AxesLabel -> {"t", "y[t]"},
Epilog -> {Red, AbsolutePointSize, Point[data]}]}]] // Quiet

Bob Hanlon

On Sat, Nov 26, 2011 at 5:09 AM, Dino <dinodeblasio at gmail.com> wrote:
> Hello everyone,
>
> I have this first order differential equation:
>
> y'[t] = -A (y[t])^2 + B (C - y[t])
>
> where A and B are unknown constants and C is known constant.
> One condition is y==0
>
> A and B should be determined by fitting a list of {y[i],t[i]} values.
>
> For this reason i would like to approximate my differential equation
> with a function which I could use to fit the data and find A and B.
>
> I don't know how to do this.
> Any help is highly appreciated.
>
> Thanks,

```

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