y + (x) y + (x) y = f (x) .
y + (x) y + (x) y = 0
= + (5.6)
= + + +
= + + +
(5.1)
+ + + + (x) + +
(x) + = f (x)
+ + + + (x) +
(x) + = f (x)
= W (x) 0
= (x)
= (x)
(5.6)
(5.2):
y + (x) y + (x) y = f (x) 2- :
f(x) = (x) + (x),
u -
+ (x) y + (x) y = (x)
+ (x) y + (x) y = (x)
() + ) + ) = + + + () + ) + = (x) + (x) = f(x)
10. .
11. .:
. :
a (x), b (x), c (x) − , x.
(, ) . .
. :
: y 1 ,
, y = y 1 + u , :
, y 1 − , . u (x):
( )
,
:
y =
+ p(x) + p (x) z + q (x) * + q (x) * 2 z + q (x) = f (x)
+ p(x) z + 2q (x) z +q(x) = 0
+z (p (x) + 2q (x) ) + q (x) =0
n=2
12. .:
13. .:
14. . .
15. n . . .:
16. . :
.
17. . :
: 2- : y + p y + q y = f(x) (5.7) , :1. f(x) = , - n. 2.f(x) = ( cos β x + (x) sin β x). f(x) . - (5.1). . 1: (5.7) :f(x) = α R - n. - (5,7) : y + p y + q y = (5.8) - : = Qn (x) (5.9) r = α - + p k + q = 0,.. r , α - - + p k + q = 0, Qn (x) = + + . + An n, Ai (i= 0, 1, 2,n) ) α -: + p k + q = 0,.. α , r = 0 = Q n (x) ) α () - + p k + q = 0, α = r = 1, = x Q n (x) ) α = 2- - + p k + q = 0, r = 2 = Q n (x) 2: (5.7) :f(x) = () cosβx + Q m (x) sin β (x), ) Qm (x) n m , α β - , - (5.7) y + py + qy = () cosβx + Qm (x) sinxβ) (5.10) : = * (Ml (x) cosβx + N l (x) sin βx) (5.11) r- (α + βi) : + pk + q = 0, Me (x) Ne (x)- l . l ) Qm (x), l =max(n,m). 1: (5.11) (5.10) , . -. 2: (5.11) ) 0 Qm (x) 0. 3: - (5.7) 1 2, (5.2) . (5.2): : - (5.1) 2- :f(x) = (x) + (x), u - - + (x) y + (x) y = (x) + (x) y + (x) y = (x) -. - (n . n- + (x) + (x) + + (x)y = f(x) (x), , (x), f(x) (, b). . - + (x) + + (x)y = 0. y n- = y= . = + + + yi(x) - . i(x) - + + + = 0 + + + = 0 + + + = 0 + + + = f (x) n- , f(x) , -. y + + + y = f (x) R, f (x) n=2.
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18. . .:
19. . :
20. .: