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Publié par | mijec |
Nombre de lectures | 20 |
Langue | Français |
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1 2
1 2
R
1
y_ =a(t)y+b(t); y(t = 0) =y ;0
a b R
y_ =a(t)y:
Rt
a(s)ds
0v(t) = u(t)e
v u_ = 0
Rt
a(s)ds
0v :t7!Ce ;
C
_ =a +b
Rt
a(s)ds
0y(t) = (y (0))e +(t):0
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Rt
a(s)ds
0(t) =u(t)e :
R
t
a(s)ds_ 0 = a +b u_ = b(t)e
Z tR Rt t
a(s)ds a(s)ds
0 y(t) =y e + b()e d :0
0
a(t) a(t) = a
Z t
at a(t )y(t) =y e + b()e d :0
0
tb(t) = e P(t) P
t(t) = Q(t)e
P = Q =a Q = P +1 =a
Q
at ty(t) = (y Q(0))e +Q(t)e :0
t 2a(t) = 1 b(t) = 2et
t 2_(t) = Q(t)e Q = 2 2Q+Q = 2t
12Q(t) =t t+ :
2
1 1t 2 ty(t) = y e + t t+ e:0
2 2
2
y=a(t)y_ +b(t)y+c(t); y(t = 0) =y ; y_(t = 0) =v ;0 0
a b c R
y=a(t)y_ +b(t)y:
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0 0v (t )v (t ) v (t )v (t ) = 0;1 0 0 0 2 02 1
t 2R0
a = 0 b = 1 v = cost v = sint1 2
_ =a(t)+b(t)+c(t)
y(t) =v +v + ;1 2
_v (0)+