deTaylor

[fhub]

(05-22-2015 08:31 PM)salvomic Wrote:  Parisse has already added the solution for y'=(x+y)^2 in XCas, but it was after the last FW was ready. I hope this will be added in the next firmware.
In the meantime your deTaylor is helpful also for this equation ;-)

Well, in the meantime you could also use the following function:

Code:


deLinSubst(f,x,y):=
BEGIN
  local k;
  k:=simplify(diff(f,x)/diff(f,y));
  IF diff(k,x)<>0 or diff(k,y)<>0 THEN
    RETURN("No linear substitution!");
  END;
  RETURN(solve(subst(integrate(1/(subst(f,y=y-k*x)+k),y),y=y+k*x)=x+G_0,y));
END

Works only for ODEs of the type y'=f(a*x+b*y+c) with a,b,c=const.
For your example y'=(x+y)^2 just enter:
deLinSubst((x+y)^2,x,y)
(enter only the RHS, not y'=...)

In this simple form you get a solution only if Xcas can 'solve' the equation for y, but it could easily be modified to return at least an implicit solution if the equation is unsolvable.

Franz