/*
 * This file:
 *   http://anggtwu.net/MAXIMA/2024-2-C2-EDOVS.mac.html
 *   http://anggtwu.net/MAXIMA/2024-2-C2-EDOVS.mac
 *          (find-angg "MAXIMA/2024-2-C2-EDOVS.mac")
 * Author: Eduardo Ochs <eduardoochs@gmail.com>
 *
 * (c2m242p2p 3 "questao-1")
 * (c2m242p2a   "questao-1")
 *
 * Superseded by:
 *   (find-angg "MAXIMA/2025-1-s.mac" "EDOVS-tests")
 *
 * (defun e () (interactive) (find-angg "MAXIMA/2024-2-C2-EDOVS.mac"))
*/



/* (find-myqdraw "myqdraw3.mac")
*/
load_myqdraw();

EDOVS_M() := matrix(
  ['diff(y,x), "=", g(x)/h(y)],
  [h(y)*del(x), "=", g(x)*del(x)],
  ['integrate(h(y),y), "=", 'integrate(g(x),x)],
  [H(y)+C1, "=", G(x)+C2],
  [H(y), "=", G(x)+C3],
  [Hinv(H(y)), "=", Hinv(G(x)+C3)],
  ["||", "", ""],
  [y, "", ""])$



/*
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-EDOVS.mac");
M0 : EDOVS_M();

G(x) := -x^2;
G(x) := -4*x^2;
H(y) :=  y^2;
define(g(x), diff(G(x),x));
define(h(y), diff(H(y),y));
Hinv(u) := sqrt(u);
M : EDOVS_M();
e1    : M[1][1] = M[1][3];
sols  : ode2(e1,y,x);
solss : solve(sols,y);
solsn : solss[1];
solsp : solss[2];
sol1  : y = M[6][3];
e2    : subst(sol1, e1);
e3    : ev(e2,diff);

[xmin,ymin, xmax,ymax] : [-3,-3, 3,3];

define(F(x,y), H(y)-G(x));
tracinhos : directionfield(h(y),g(x), lc(red))$
myqdraw(xyrange(), tracinhos);
myqdraw(xyrange(), myimp1(F(x,y)=1), myimp1(F(x,y)=4));

e1;
sol1;
e4 : subst([x=2,y=3], sol1);
solve(e4, C3);

F(x,y);


** VS:
* (eepitch-maxima)
* (eepitch-kill)
* (eepitch-maxima)
load("2024-2-C2-EDOVS.mac");
M0 : EDOVS_M();

G(x) := -(x-1)^2;
H(y) :=  (y+1)^2;
define(g(x), diff(G(x),x));
define(h(y), diff(H(y),y));
hinvs : solve(x = H(y), y);
define(Hinvn(x), rhs(hinvs[1]));
define(Hinvp(x), rhs(hinvs[2]));
Hinvp(H(x));
Hinvn(H(x));
factp : y+1 >= 0;
factn : y+1 <= 0;
forget(factp); assume(factn); define(Hinv(u),Hinvn(u)); Hinv(H(y));
forget(factn); assume(factp); define(Hinv(u),Hinvp(u)); Hinv(H(y));
Hinv(H(y));

M : EDOVS_M();
e1    : M[1][1] = M[1][3];
sols  : ode2(e1,y,x);
solss : solve(sols,y);
solsn : solss[1];
solsp : solss[2];
sol1  : y = M[6][3];
e2    : subst(sol1, e1);
e3    : ev(e2,diff);

[xmin,ymin, xmax,ymax] : [-3,-3, 3,3];

define(F(x,y), H(y)-G(x));
tracinhos : directionfield(h(y),g(x), lc(red))$
myqdraw(xyrange(), tracinhos);
myqdraw(xyrange(), myimp1(F(x,y)=1), myimp1(F(x,y)=4));

e1;
sol1;
e4 : subst([x=2,y=3], sol1);
e4 : subst([x=1,y=-2], sol1);
solve(e4, C3);

F(x,y);



*/




/*
 * Local Variables:
 * coding:  utf-8-unix
 * End:
*/