Subject: Change of variable for differential equation
From: Daniel Lakeland
Date: Sun, 17 Jun 2007 14:50:40 -0700
On Sun, Jun 17, 2007 at 03:07:12PM -0400, sen1 at math.msu.edu wrote:
> 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.
Unfortunately, the example operation I gave was mostly just
example... The real situations might involve a nonlinear differential
equation or what have you. The goal being to be able to transform from
a fairly general differential equation on an x coordinate to a related
equation on a t coordinate that is a simple scaling and translation of
x.
so for example something ugly like
diff(h(x),x) - diff(h(x),x,2)*atan(diff(h(x),x)) = g(x)
where I'd prefer to have maxima calculate the appropriate expression
for the change of variable on the left because I'm lazy :-)
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan