# dfdt: Right Side of a first order ODE In nlsrk: Runge-Kutta Solver for Function nls()

## Description

Gives the value of the right side of a first order Ordinary Differential Equation Used in frunge (Numeric resolution using Runge-Kutta 4 metthod)

## Usage

 `1` ``` dfdt(t, y, param) ```

## Arguments

 `t` time, independent variable `y` values of the unknown function at t `param` numeric vector : the set of parameters defining the function

## Details

the unique expression composing the body of dfdt is intended as the right side of the first order differential equation :

dy/dt = dfdt(t,y,param)

The function body has to be written by the user.
param must take the form c(param1,param2,param3). if the initial value (y0) is used as a parameter (for model fitting for instance), it must be the last in the list and not used in dfdt.

## Value

a single float numeric value : the derivative of the unknown function at time t.

## Note

When used as argument for frunge, the initial condition y0 may be used as a parameter subject to fitting by `nls`, for instance. In this condition, y0 must appear as the last parameter in param and must not be used nor modified in `dfdt`

## Author(s)

Jean-Sebastien Pierre
[email protected]

## References

Any textbook in mathematics

`frunge`, `nls`
 ```1 2 3``` ```## Solves and draws the logistic function using default dfdt as provided in the package frunge(t=10, param=c(r=0.1,k=100), y0=3, Dfdt = dfdt, dt = 0.01, graph = TRUE) ```