GIA'I H^E. PHU.O.NG TRNH

186)

Gia'i h^e. phu.o.ng trnh:

dt =x+ 2y−zdzdt =x−y+ 2zHD gia’i:

Phu.o.ng trnh da.c tru.ng:

^{(λ−1)(λ−2)(λ−3) = 0}

co 3 nghi^e.m

^λ

¹

^{= 1;}λ

₂

= 2; λ

₃

= 3

.

P

_1i

02−λ

_i

−1 1

u.ng vo.i

^λ

i

gia'i h^e.:

P

_2i

1 2−λ

_i

−1=P

_3i

1 −1 2−λ

_i

e

^2t

e

^3t

1

D - u.o..c

e

^t

;

. Suy ra h^e. nghi^e.m co. ba'n

x=C

₂

e

^2t

+C

₃

e

^3t



V^a.y NTQ:

y=C

₁

e

^t

+C

₂

e

^2t

z =C

₁

e

^t

+C

₂

e

^2t

+C

₃

e

^3t

.dxdt =y−5 cost