%% PhS %% fig_S_cours_ch03_equations_differentieles_02_v01.jps 40 setxunit -7 7 setxrange -7 7 setyrange tracerepere marks /Gx_min -3 def /Gx_max 3 def /Gy_min -3 def /Gy_max 3 def /pas_x 0.5 def /pas_y 0.5 def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% definitions des couleurs %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% /coul1 {120 255 div 70 255 div 9 255 div setrgbcolor} def %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% procédures %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% définition du champ de vecteur /vect_t_y { 2 dict begin /y exch def /t exch def t 1 add 2 div y mul 1 exch end } def %% parametrage de la courbe /xdet { 1 dict begin /t exch def t end } def /ydet { 1 dict begin /t exch def t 2 div dup dup mul add Exp 0.5 mul end } def %% tracé du champ de vecteurs coul1 Gx_min pas_x Gx_max { 2 dict begin /c_x exch def Gy_min pas_y Gy_max { /c_y exch def 1 setlinewidth orange [c_x c_y] {times} plot coul1 0.5 setlinewidth c_x c_y c_x c_y c_x c_y vect_t_y c_x c_y vect_t_y norme 0.4 exch div mulv addv (->) line } for end } for %% tracé de la courbe intégrale 1 setlinewidth rouge continu -4 2.2 settrange {xdet} {ydet} courbeparam %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% texte %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% setTimesItalic noir O 0 0 [1.5 dup] dltexlabel Champ de vecteurs pour $ y'(t)=f(t,y) $ où $ f(t,y)=\displaystyle\frac{1+t}{2}y $ -5 -5 [1.5 dup] drtexlabel rouge Courbe intégrale~: 2.5 6 [1.5 dup] drtexlabel $ y(t)=ke^{\frac{t}{2}+(\frac{t}{2})^2} $ 2.5 5.5 [1.5 dup] drtexlabel