Contrôle Continu n°1 d`Équations Di érentielles Licence de

6
R
(x(t) + ¨x(t) + ˙x(t)=0
¨x(0) = ˙x(0) = 1 .
˙
X(t) = AX (t)A:= 1 2
2 4 .
D=diag (λ1, λ2)λ1λ2
exp D=diag (exp λ1,exp λ2)
A
exp (tA)t∈R
R

1
2t˙x(t) = x(t)−x2(t).
x= 0 x= 1 R
(t0, x0)∈Rt06= 0
x x (t0) = x0
x(t) = x0t2
x0t2−t2
0(x0−1)
Imax t0x
(x, I) 0 ∈I
x(0) = 0 x(0) = 1
x= 1 x(0) = 1