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

Calculul simbolic al solut¸iilor sistemelor de ecuat¸ii liniare 95
Pentru acest sistem considerǎm condit¸iile init¸iale x1(1) = 1,
x2(1) = 0, determinǎm solut¸ia problemei cu date init¸iale reprezentǎm
grafic acaestǎ solut¸ie:
> sys3_Eq1:=diff(x1(t),t)=x1(t)-x2(t)+3*t^2;
sys3 Eq1 := d x1 (t) = x1 (t) − x2 (t) + 3 t2
dt
> sys3_Eq2:=diff(x2(t),t)=-4*x1(t)-2*x2(t)+2+8*t;
sys3 Eq2 := d
x2 (t) = −4x1 (t) − 2x2 (t) + 2 + 8 t
dt
> dsolve({sys3_Eq1,sys3_Eq2});
{ x1 (t) = e −3 t C2 + e 2 t C1 − t 2
x2 (t) = 4 e −3 t C2 − e 2 t C1 + 2 t + 2 t 2 , }
> dsolve({sys3_Eq1,sys3_Eq2,x1(1)=1,x2(1)=0});
{ x1 (t) = 12
5 e−2 e 2 t − 2/5 e 3 e −3 t − t 2 ,
x2 (t) = − 12
5 e−2 e 2 t − 8/5 e 3 e −3 t + 2 t + 2 t 2 }
> x1:=12/5*exp(-2)*exp(2*t)-2/5*exp(3)*exp(-3*t)-t^2:
> x2:=-12/5*exp(-2)*exp(2*t)-8/5*exp(3)*exp(-3*t)+2*t+
2*t^2:
> plot([x1,x2],t=-0.1..2,color=[red,green],style=
[line,point]);
Figura 17