22
. y'+ ρ(x) y=f (x), ρ(x) f (x) , .
, ,
,
( , )
C .
:
, RC- -[ ]
, p (x) = b, r (x) = 1.
, :
23
y''+ ρ y'+qy=f (x), ρ q , f (x) , .
:
y''+ ρ y'+qy =0, (1)
f (x) . .
K 2 + ρ K+q =0 (2)
(1).
(2) , . 1 2.
(1) D =ρ24 q (2) :
1. D >0 ( 1≠ 2), .
2. D =0 ( 1= 2= ), :
3. D <0, : , , ( 1=α+β i, 2=αβ i, β≠0), y = e α x (C 1 cosβ x + C 2 sinβ x).
1. y''y' 2 y =0.
. K 2 K 2=0, 1=1, 2=2 . y = C 1 ex + C 2 e 2 x . 3. y'' 4 y' +13 y =0.
. 24 +13=0, 1=2+3 i, 2=23 i . y = e 2 x (C 1 cos3 x + C 2sin3 x).
:
y''+ ρ x+qy=f (x), (3)
f (x) , .
(3) y (1):
.
, . (3).
1) f (x)= e α x Pn (x), Pn (x) n. , Qn (x) , Pn (x), r , , α .
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24
A B , A, B, A + B. , A1 + A5 , A 1, 5. , , , A, p (A1 + A5) = p (A1) + p (A5) = 1/6 + 1/6 = 1/3.
A: A1, A2, A3, A4, A5, A6. , 1 5 , , p (A1 + A5) = 2/6 = 1/3.
N a A, b B, A B .
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A B, (a, b), A B . AaBb. , A1B5 , , A 1, B 5.