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

196)

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

dydt =x+ 4y+e

^2t

.HD gia’i:

Nghi^e.m cu'a phu.o.ng trnh da.c tru.ng:

^r

¹

^{= 2;r}

²

^{= 3}

; tu. do du.o..c NTQ cu'a

(x = 2C

₁

e

^2t

+C

₂

e

^3t

h^e. phu.o.ng trnh thu^an nh^at la:

y =−C

₁

e

^2t

−C

₂

e

^3t

.

Bi^en thi^en hang s^o d^e' du.o..c nghi^e.m t^o'ng quat cu'a h^e. kh^ong thu^an nh^at:

x = 2C

₁

e

^2t

+C

₂

e

^3t

−32e

^t

+ 2te

^2t

y =−C

₁

e

^2t

−C

₂

e

^3t

+ 12e

^t

−(t+ 1)e

^2t

.dxdt = 2x+y