input geometrie2d;
 input courbes;
 input graph;
 input plusa;
 
 %@ode'système:ed1.ode
 % y'= t - exp(y)
 % y = $2 
 % print t, y
 % step $1, $3
 %@ode'solution: ed1-1 -4 3 5
 %@ode'solution: ed1-2 -3 3 5
 %@ode'solution: ed1-3 -2 3 5
 %@ode'solution: ed1-4 -1 3 5
 %@ode'solution: ed1-5  0 3 5
 %@ode'solution: ed1-6  1 3 5
 %@ode'solution: ed1-7  2 3 5
 %@ode'solution: ed1-8  3 3 5 
 %@ode'solution: ed1-9  4 3 5
 
 vardef trajectoire (expr f) =
     save s; gdata(f, s, if i>1:..fi (scantokens s1,scantokens s2))
 enddef;
 
 vardef F(expr x,y) = x - exp(y) enddef;
 
 

 beginfig(1);
 
     Repere(12,9,5,4.5,1.5,1.5);
     Axes;
     Debut;
 	Unites(1);
 	Graduations;
 
 	% Tracé du champ de vecteurs
 	ahlength := 2;
 	ChampVecteurs(F,0.2,0.2,0.4,0.4,0.15,0.5white); 
 
 	trace Representation(ln,0.05,5,50)
 	    withpen pencircle scaled 1
 	    withcolor (0.8,0.2,0.5);
 
 	for i=1 upto 9:
 	    trace trajectoire("ed1-" & decimal i)
 		withcolor (0.1,0.6,0.1);
 	endfor
 	
 	Etiquette.rt("$y=\ln x$",1.5,(0.25,-2));
 	paLegendeCCO((-1.5,1.75),"$y'=x-e^{y}$");
     Fin;
     
 endfig;
 
 vardef F(expr x,y) = -2x*y/(x*x+y*y) enddef;
 
 %@ode'système:ed2.ode
 % y' = -2*t*y/(t*t+y*y)
 % y  = $2
 % print t, y
 % step $1, $3
 
 %@ode'eval: 
 % for($i=1;$i<=10;$i++) { solution("ed2-$i",-4,-2.25+$i/2,4); }
 
 

 beginfig(2);
 
     Repere(12,9,6,4.5,1.5,1.5);
     Axes;
     Debut;
 	Unites(1);
 	Graduations;
 
 
 	% Tracé du champ de vecteurs
 	ahlength := 2;
 	ChampVecteurs(F,0.2,0.2,0.4,0.4,0.15,0.5white); 
 
 	
  	for i=1 upto 10: 
 	    trace trajectoire("ed2-" & decimal i) withcolor (0.1,0.6,0.1); 
 	endfor
 
 	paLegendeCCO((0,-2.25),"$(x^2+y^2)y'+ 2xy = 0$");
 	
     Fin;
     
 endfig;
 
 %@ode'système:ed3.ode
 % y' = 2*t*y + y*y
 % y = $2
 % print t, y
 % step $1, $3
 
 %@ode'solution: ed3-1 -2 3 1
 %@ode'solution: ed3-2 -3 3 2.8
 
 vardef F(expr x,y) = 2x*y + y*y enddef;
 
 

 beginfig(3);
 
     Repere(12,9,6,4.5,1.5,1.5);
     Axes;
     Debut;
 	Unites(1);
 	Graduations;
 
 	trace Droite(origin,(1,-2)) withcolor (0.5,0.2,0.3);
 	
 	% Tracé du champ de vecteurs
 	ahlength := 2;
 	ChampVecteurs(F,0.2,0.2,0.4,0.4,0.15,0.5white); 
 
 	for i=1 upto 2:
 	    trace trajectoire("ed3-" & decimal i) withcolor (0.1,0.6,0.1);
 	endfor
 	
 	paLegendeCCO((0,-2.25),"$y'=2xy+y^2$");
 	
     Fin;
     
 endfig;
 
 end