Weird dsolve behaviour
Ray Vickson
(2*sqrt(3)))^2. Defining g first and setting de:= diff(f(t),t) = -f(t)
^2 + g, we have that sol:=dsolve(de,f(t)) fails: it gives
sol := (6*f(t)*b-f(t)*3^(1/2)*t-2*3^(1/2))^((12*b^2-4*b*t*3^(1/2)+t^2)/
(2*b*3^(1/2)-t)/(6*b-t*3^(1/2)))*(6*f(t)*b-f(t)*3^(1/2)*t+3*3^(1/2))^(-
(12*b^2-4*b*t*3^(1/2)+t^2)/(2*b*3^(1/2)-t)/(6*b-t*3^(1/2)))*(6*b-t*3^
(1/2))^(-5*(12*b^2-4*b*t*3^(1/2)+t^2)/(2*b*3^(1/2)-t)/(6*b-t*3^(1/2)))-
_C1 = 0,
which is an implicit equation in f(t) that Maple cannot solve.
However, after restarting and writing the de directly (that is,
substituting the actual formula for g into the de), sol:=dsolve(de,f
(t)) gives
sol := f(t) = (-30*3^(1/2)*b*t^4+3*t^5+2*_C1-720*3^(1/2)*b^3*t^2-864*3^
(1/2)*b^5+360*b^2*t^3+2160*b^4*t)/(-12*3^(1/2)*b*t^5+t^6-t*_C1+2*_C1*3^
(1/2)*b-480*3^(1/2)*b^3*t^3-1728*3^(1/2)*b^5*t
+180*b^2*t^4+2160*b^4*t^2+1728*b^6),
which is an explicit formula for f(t).
Why should it matter whether g is defined through a prior formula or
input directly? Maple prints out *exactly* the same de on the screen
in both cases!
R.G. Vickson
Robert Israel
There are many cases where a computation may take different paths; different
sessions (even with exactly the same input) may produce different results.
For example, it may depend on exactly how various objects are placed in
memory.
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Ray Vickson
Yes, but I get the indicated behaviour consistently. It happens in
several independent sessions, and using several 'restarts' within the
same session.
R.G. Vickson