# [Maxima] Change of variable for differential equation

sen1 at math.msu.edu sen1 at math.msu.edu
Sun Jun 17 14:07:12 CDT 2007

```There is no 'h' on the rhs, so all you have to do is:

dh/dt = dh/dx *dx/dt = dh/dt * a = g(a*t + b)

So,
dh/dt = (1/a)* g(a*t + b)

Once you have this, higher derivatives are no problem.

HTH,
-sen

On Sun, 17 Jun 2007, Daniel Lakeland wrote:

> Suppose I have a differential equation such as
>
> deq: diff(h(x),x) = g(x);
>
> I want to express solutions in terms of a nondimensional variable t
> where x depends on t via an affine transformation.
>
> xeqn: x = a*t-b;
>
> how can I most easily accomplish the transformation of this
> differential equation into an equation in terms of t?  Preferrably I
> would like to accomplish this in an automated way rather than a lot of
> by-hand substitutions (the actual equations might be significantly
> more complicated)
>
> It obviously doesn't work to simply say subst(xeqn,deq) because I wind
> up with something like this:
>
> 			 d
> (%o3) 		      -------- (h(a t - b)) = g(a t - b)
> 		      da t - b
>
> Is there a way to convert that funky differential operator to an
> application of the chain rule? how about for higher derivatives?
>
>

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