Subject: simplify d(a^2*y^2)/d(a*y) with a constant
From: Barton Willis
Date: Thu, 9 Jun 2011 06:13:07 -0500
The easiest way for me to to this is to use the (optional) positional derivative package.
Example: For the DE m * diff(f(t),t,2) = k * f(t), substitute f(t) = g(omega * t). After
that, choose omega:
(%i1) load('pdiff)$
(%i2) m * diff(f(t),t,2) = k * f(t), f(t) := g(omega * t);
(%o2) m*omega^2*g[(2)](omega*t)=k*g(omega*t)
(%i3) ratsubst(t,omega*t,%);
(%o3) m*omega^2*g[(2)](t)=k*g(t)
(%i4) de : first(solve(%,diff(g(t),t,2)));
(%o4) g[(2)](t)=(k*g(t))/(m*omega^2)
(%i5) solve(1=coeff(rhs(de), g(t)),omega);
(%o5) [omega=-sqrt(k/m),omega=sqrt(k/m)]
(%i6) subst(second(%),de);
(%o6) g[(2)](t)=g(t)
--Barton (author of pdiff)
-----maxima-bounces at math.utexas.edu wrote: -----
>To:?maxima at math.utexas.edu
>From:?c?dric?ody?<cedric.listes at gmail.com>
>Sent?by:?maxima-bounces at math.utexas.edu
>Date:?06/09/2011?03:09AM
>Subject:?[Maxima]?simplify?d(a^2*y^2)/d(a*y)?with?a?constant
>
>Dear?list-users,
>
>I?would?like?to?know?if?it?is?possible?to?use?Maxima?to?non-dimensionalize
>a?differential?equation.
>
>Let?say?I?have?the?expression
>
>expr:x+d(x^2)/dx
>
>I?want?to?replace?x?by?y?with?y=a*x
>
>
>I?have?used?the?following?to?do?that
>
>subst(a*y,x,expr);
>
>The?answer?is?
>
>a*y+d(a^2*y^2)/d(a*y)
>
>Is?it?possible?to?simplify?the?last?term?since?a?is?constant?
>
>Thank?you
>
>C?dric
>
>
>
>
>
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