kill(all)$

biotech :appendix 1: second order ode : coef D,c  ,version  1.0
peter.vlasschaert@gmail.com,08/05/2020

load packages
============

load(contrib_ode);

load(lrats);

differential equation :model :'second order ode'
====================
ode = (o)rdinary (d)ifferential (e)quations

assume(D>0,c>0);

p1:D*'diff(u,z,2)+c*'diff(u,z)+u=0;

D: diffusion coef.
c : wave speed
=================
rem : u = u(z),depends
=================

conditional solution
===============

info :1e) c^2 > 4*D,2e)  c^2 < 4*D, 3e)c^2 =4*D

question maxima ask :give three possibilities, to avoid this question use 'assume'

1e) c^2 > 4*D
===========

assume(c^2>4*D);

p1a:ode2(p1,u,z);

result : value under sqrt pos :real 

forget : use to kill assume

forget(c^2>4*D);

2e) c^2 < 4*D
===========

assume(c^2<4*D);

p1b:ode2(p1,u,z);

result : value under sqrt pos :complex

pa:forget(c^2<4*D);

3e) c^2 = 4*D
===========

=>  search google :assume and equal in maxima

see: https://sourceforge.net/p/maxima/mailman/message/35353113/

p1c:assume(equal(c^2,4*D));

p1c1:ode2(p1,u,z);

forget(equal(c^2,4*D));;

question: c^2= 4*D
===============

 => true ,false , 'is' ,command maxima

limiting value 
==========
c = 2*sqrt(D)

p2:is(c^2=4*D);

reason : forget 'pa' ,see above ' %o13'