substitute for independent variable in 'diff

maxima-bounces at math.utexas.edu wrote on 10/10/2011 10:00:09 AM:


> I looked at pdiff but the examples are complicated enough that I 
> haven't figured out how to apply it to this case. 

Sorry about the overly complicated examples in pdiff :(  A minimalist 
example:

(%i1) load(pdiff)$

A DE

   (%i2) de : diff(f(x),x) = 42 * f(x); 
   (%o2) f[(1)](x)=42*f(x)

Let f(x) = g(42 * x)

   (%i3) de, f(x) := g(42 * x);
   (%o3) 42*g[(1)](42*x)=42*g(42*x)

Replace 42 * x by x

  (%i4) ratsubst(x, 42*x,%);
  (%o4) 42*g[(1)](x)=42*g(x)

And, if you like, solve for diff(g(x),x)

  (%i5) solve(%, diff(g(x),x));
  (%o5) [g[(1)](x)=g(x)]

So the DE for g is diff(g(x),x) = g(x).


--Barton (author of pdiff)