Subject: [1] enter (in console) ; [2] implicit functions
From: Stavros Macrakis
Date: Fri, 28 Sep 2012 12:04:35 -0400
(I also want to use M to ascertain whether dy/dx > 0 .)
Does this help:
(%i27) y + log(y) + x = 0;
(%o27) log(y)+y+x=0
(%i28) diff(%);
(%o28) (1/y+1)*del(y)+del(x)=0
(%i29) ratsubst(dydx,del(y)/del(x),%); <<< doesn't always produce 'clean'
result, but does in this case
(%o29) (((dydx+1)*y+dydx)*del(x))/y=0
(%i30) solve(%,dydx);
(%o30) [dydx=-y/(y+1)]
(%i31) load(to_poly_solve)$
(%i32) %solve([%o3,dydx>0],[x,y,dydx]);
(%o32)
%union([0<dydx,del(x)=0],[dydx=-((dydx+1)*y)/(y+1),-(dydx+1)*y*(y+1)>0])
(%i33) solve(%o3,dydx);
(%o33) [dydx=-y/(y+1)]
(%i34) part(%,1,2);
(%o34) -y/(y+1)
(%i35) %solve(%>0,y);
(%o35) %union([-1<y,y<0])