Capitolul 1 Ecuatii diferentiale de ordinul ˆıntâi rezolvabile prin ...

94 CAPITOLUL 3
> sys2_Eq1:=diff(x1(t),t)=-x1(t)-x2(t);
sys2 Eq1 := d x1 (t) = −x1 (t) − x2 (t)
dt
> sys2_Eq2:=diff(x2(t),t)=-x2(t)-x3(t);
sys2 Eq2 := d
x2 (t) = −x2 (t) − x3 (t)
dt
> sys2_Eq3:=diff(x3(t),t)=-x3(t);
sys2 Eq3 := d x3 (t) = −x3 (t)
dt
> dsolve({sys2_Eq1,sys2_Eq2,sys2_Eq3},{x1(t),x2(t),x3(t)});
{ x1 (t) = 1/2 ( C3 t 2 − 2 C2 t + 2 C1) e −t ,
x2 (t) = − ( C3 t − C2)e −t ,
x3 (t) = C3 e −t }
> dsolve({sys2_Eq1,sys2_Eq2,sys2_Eq3,x1(0)=1,x2(0)=0,
x3(0)=2});
{ x1 (t) = 1/2 (2 t2 + 2) e−t x2 (t) = −2 te−t ,
x3 (t) = 2 e−t }
> plot([1/2*(2*t^2+2)*exp(-t),-2*t*exp(-t),2*exp(-t)],
t=-1.3..8,colour=[green,black,blue],thickness=[3,4,1],
style=[line,point,line]);
Figura 16
3. Sistemul de douǎ ecuat¸ii diferent¸iale liniare cu coeficient¸i constant¸i neomogen:
˙
x1 = x1− x2+ 3t2 x2 ˙ = −4x1− 2x2+ 2 + 8t
(3.15)