( )

yi(X)

(3) y(N)+ P1y(N-1)+ ... + Pny = fi(X) = ?1y1+ ?2y2 + ... + ?nyn, y(n)+ P1y(n-1)+ ... + Pny = ?1 f1(X) + ?2 f2(X) + ... + ?n fn(X) (4)

-: n = 2

y = ?1y1+ ?2y2

y '= ?1y1'+ ?2y2'

y '' = ?1y1'' + ?2y2''

ϳ y, y ', y ", (4), y1 y2 (3)

?1y1"+ ?2y2"+ P1(X) [?1y1'+ ?2y2'] + P2(X) [?1y1+ ?2y2] =

= [?1y1"+ P1(X) ?1y '1+ P2(X) ?1y1] + [?2y2"+ P1(X) ?2y '2+ P2(X) ?2y2] = ?1f1(X) + ?2f2(X)

16. -

, - .

2- . y "+ P1(X) y '+ P2(X) y = f (x) (1) y1(X) y2(X) -

y "+ P1(X) y '+ P2(X) y = 0 (X) = C1y1(X) + C2y2(X) (2). y * (x) (14) C1 C2 , x.

y * = C (X) y (X) + C (X) y (X), y * = C ' (X) y (X) + C (x) y ' (X) + C ' (X) y (X) + C (x) y ' (X)

C (X) C (X) C ' (X) y (X) + C ' (X) y (X) = 0 / (3), y * '= C (X) y ' (X) + C (X) y ' (X); y * "= C (X) y ' (X) + C (X) y " (X) + C ' (X) y ' (X) + C (X) y " (X).

ϳ y *, y * ', y * " (1): C (X) [y " (X) + P (X) y '(X) + P (X) y (X)] + C (X) [y " (X) + P (X) y '(X) + P (X) y (X)] + C ' (X) y ' (X) + C ' (X) y ' (X) = f (x). y (X), y (X) , [] = 0 C ' (X) y ' (X) + C ' (X) y ' (X) = 0.

(3):

C '1(X) y1(X) + C '2(X) y2(X) = 0

C '1(X) y '1(X) + C '2(X) y '2(X) = f (x) (4)

C '1(X) C '2(X).

: W [y1, y2] = 0 , C (X) = (X), C (X) = (X) C1(X) C2(X) . ϳ y *.

n- - Ci(X) :

C ' (X) y + C ' (X) y + ... + C ' (X) y = 0

C ' (X) y ' + C ' (X) y ' + ... + C ' (X) y ' = 0

... .

C ' (X) y + C ' (X) y + ... + C ' (X) y = 0

C ' (X) y + C ' (X) y + ... + C ' (X) y = F (x)




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