TM NGHI^E.M T^O'NG QUAT CU'A H^E. PHU.O.NG TRNH

200)

Tm nghi^e.m t^o'ng quat cu'a h^e. phu.o.ng trnh:

dzdx =z−4y.HD gia’i:

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

^{(λ−1)(λ−2) = 0}

, gia'i ra

^λ

¹

^{= 1;λ}

²

^{= 2}

. Tu. do

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

e

^x

2e

^2x

;.−e

^x

−3e

^2x

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

(y =C

₁

e

^x

+ 2C

₂

e

^3x

z =−C

₁

e

^x

−3C

₂

e

^2x

.dxdt = 2x−3y