peuille d9exer™i™e n¦Q Équ—tions différentielles

y00 + 2y0+y= 2e−xE
λ y0Ry0(x) = λx2e−x
E
yR R E
z z =y−y0E1
u00 + 2u0+u= 0
t=u0+u t0+t= 0
E1
E
f E (O,~ı, ~ )
(−1,0) ~ı
y0+ 2y= 4e1−2xE
fRf(x) = 4xe1−2x
E
y0+ 2y= 0 (E0)
gRE g −f
(E0)
g E
g0E−2e0
(E)y00 −2y0+y=x2
f(x) = x2+ 4x+ 6 (E)
f2 (E)
g(x) = (2x−5)ex+x2+ 4x+ 6 (E)
•f0+ 2f= 0 f(1) = 3 •3f0−2f= 0 f(3) = −1
•2f0=f2f(−1) = 3 •f−2f0= 0 f(0) = 3

i t
(Eq)
Li0(t) + Ri(t) = E
L R
E
+
−
L= 0,2H R = 100Ω E= 10V(Eq)
t= 0
i(t)t+∞