# A cute little bit of Maple code to determined whether or not a 
# DE is separable.
# 
# Let y' = F(x,y) be a 1st order DE
# 
# Then "checkseparable(F)" should return true if it determines the DE is separable 
# otherwise it may or may not be separable.  However, it returns an idea for a second 
# attempt.
# 
> checkseparable:=proc(F) \
  local g,d2gdxdy;\
  g:=log(F);\
  d2gdxdy:=simplify(diff(g,x,y));\
  if d2gdxdy=0 then \
     RETURN(true) \
  else\
    RETURN(`it seems not to be separable. You might want to plot diff( log(F),x,y). If the plot is zero everywhere in the plot, then the DE may well be separable after all.`)\
  fi \
end;

checkseparable :=

proc(F)
local g,d2gdxdy;
    g := log(F);
    d2gdxdy := simplify(diff(g,x,y));
    if d2gdxdy = 0 then RETURN(true)
    else
        RETURN(
        `it seems not to be separable. You might want to plot diff( log(F),x,y). If the plot i\
        s zero everywhere in the plot, then the DE may well be separable after all.`
        )
    fi
end

--------------------------------------------------------------------------------
> checkseparable(y+y^2);\


                                      true
--------------------------------------------------------------------------------
> checkseparable(1+x+y+x*y);\


                                      true
--------------------------------------------------------------------------------
> checkseparable(sin(x*y));

it seems not to be separable. You might want to plot diff( log(F),x,y). If the \
plot is zero everywhere in the plot, then the DE may well be separable after al\
l.
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>