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

183)

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

dt =y−x+zdzdt =x−z1−λ −2 −1−1 1−λ 1= 0⇔λ(λ

²

−λ−2) = 0HD gia’i:

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

1 0 −1−λ⇔λ

₁

= 0, λ

₂

=−1, λ

₃

= 2P

_1i

1−λ

_i

−2 −1

Vo.i cac

^λ

ⁱ

^{; i= 1,2,3}

gia'i h^e.:

−1 1−λ

_i

1P

_2i

= 0P

_3i

1 0 −1−λ

_i

D - ^e' tm nghi^e.m ri^eng tu.o.ng u.ng. Tu. do suy ra h^e. nghi^e.m co. ba'n:

x

₁

= 1, y

₁

= 0, z

₁

= 1; x

₂

= 0, y

₂

=e

^−t

, z

₂

=−2e

^−t

; x

₃

= 3e

^2t

,y

₃

=−2e

^−2t

, z

₃

=e

^2t

.

x=C

₁

+ 3C

₃

e

^2t



V^a.y h^e. nghi^e.m t^o'ng quat:

y=C

₂

e

^−t

−2C

₃

e

^2t

z =C

₁

−2C

₂

e

^−t

+C

₃

e

^2t

dxdt −5x−3x= 0