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/* Solution of first order ODEs by factoring
References:
Daniel Zwillinger, Handbook of Differential Equations, 3rd ed
Academic Press, (1997), pp 265-266
Copyright (C) 2004 David Billinghurst
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
put('ode1_factor,001,'version)$
ode1_factor(eq,y,x):= block(
[de,%p,ans:[],s,inflag:true,powflag:true,u,factors:[]],
ode_disp(" in ode1_factor"),
/* substitute %p=y' */
de: expand(lhs(eq)-rhs(eq)),
de: subst(%p,'diff(y,x),de),
/* At present restricted to simple cases such as p^2+5p+6=0
What about repeated factors? */
/* if ( not(freeof(x,y,de)) ) then return(false), */
de:factor(de),
/* fail if the ode wasn't simplified by factoring */
if ( not(inpart(de,0)="*") or is(length(de)<2) ) then (
ode_disp2(" cannot factor",de),
return(false)
),
/* Count the factors that are DEs. There may be constant terms
Some test cases failed when this was combined with the loop below */
for u in de do (
if not(freeof(%p,u)) then (
factors:endcons(u,factors)
)
),
if length(factors)<2 then (
ode_disp2(" cannot factor",de),
return(false)
),
ode_disp2(" and after factoring is ",de),
for u in de do (
/* Do not continue for higher order terms (including repeated factors) */
if hipow(expand(u),%p)>1 then (
ode_disp2(" unsuitable term ",u),
powflag:false
)
),
if powflag=false then return(false),
/* For each factor, try and solve ODE */
for u in factors do (
ode_disp2(" Factor ",u),
if not(freeof(%p,u)) then (
s:ode2(subst('diff(y,x),%p,u)=0,y,x),
ode_disp2(" has solution",s),
if s#false then ans:endcons(s,ans)
)
),
if ans#[] then (
method:'factor,
ans
)
else
false
)$
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