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

199)

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

dt =−x+ 5y−zdzdt =x−y+ 3z.HD gia’i:

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

^λ

³

^−11λ

²

^{+ 36λ−36 = 0}

, gia'i ra

^λ

1

= 2;λ

₂

=3;λ

₃

= 6

. Tu. do du.o..c ba h^e. nghi^e.m co. ba'n:

−e

^2t

e

^2t

0e

^3t

.;−2e

^6t

e

^6t

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

x =C

₁

e

^2t

+C

₂

e

^3t

+C

₃

e

^6t

y =C

₂

e

^3t

−2C

₃

e

^6t

z =−C

₁

e

^2t

+C

₂

e

^2t

+C

₃

e

^6t

.dydx =y+z