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

193)

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

dzdx = 2z+ 4y+e

^2x

.HD gia’i:

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

^λ

²

^{−4λ+ 8 = 0.}

Khi do

^λ

1

= 2 + 2i, λ

₂

= 2−2i.

H^e. thu^an nh^at co nghi^e.m

y =e

^2x

(C

₁

cos 2x+C

₂

sin 2x), z=−2e

^2x

(C

₂

cos 2x−C

₁

sin 2x).

Va nghi^e.m cu'a h^e. kh^ong thu^an nh^at

y=e

^2x

(C

₁

cos 2x+C

₂

sin 2x)− 14e

^2x

, z =−2e

^2x

(C

₂

cos 2x−C

₁

sin 2x).dydx = 2y+z+e

^x