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

92 CAPITOLUL 3
> dsolve(sys1_Eq1,sys1_Eq2,x1(0)=1,x2(0)=1,x1(t),x2(t));
{x2 (t) = 5/6 e 3t + 1/6 e −3t ,x1 (t) = 5/3 e 3t − 2/3 e −3t }
> sol_x1:=5/3*exp(3*t)-2/3*exp(-3*t):
> sol_x2:=5/6*exp(3*t)+1/6*exp(-3*t):
> plot([sol_x1,sol_x2],t=0..1,color=[red,blue],
style=[line,point]);
Figura 13
Solut¸ia problemei cu date init¸iale asociatǎ acestui sistem va fi consideratǎ
> with(DEtools):
> DEplot(sys1_Eq1,sys1_Eq2,x1(t),x2(t),t=0..1,
> [[x1(0)=1,x2(0)=1]],x1=0..40,x2=0..20,scene=
[x1(t),x2(t)]);
Figura 14