HA~Y TM NGHI^E.M T^O'NG QUAT CU'A PHU.O.NG TRNH

127)

Ha~y tm nghi^e.m t^o'ng quat cu'a phu.o.ng trnh:

^y

⁰⁰

^−2y

⁰

^{+ 2y=x(e}

^x

^{+ 1)}HD gia’i:

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

^λ

²

^{−2λ+ 2 = 0⇐⇒ λ}

¹

^{= 1±i}

. Nghi^e.m t^o'ng quat

cu'a phu.o.ng trnh tuy^en tnh thu^an nh^at tu.o.ng u.ng:

^{y = e}

^x

^(C

1

cosx+C

₂

sinx)

. Tm

nghi^e.m ri^eng da.ng:

^y

^∗

^=y

¹

^+y

²

; vo.i

^y

1

la nghi^e.m ri^eng cu'a

^y

⁰⁰

^−2y

⁰

^{+ 2y=xe}

^x

, co da.ng

y

1

=e

^x

(Ax+B) =⇒ A= 1;B = 0

va

^y

²

la nghi^e.m ri^eng cu'a

^y

⁰⁰

^−2y

⁰

^{+ 2y =x}

, co da.ng

y

₂

=A

⁰

x+B

⁰

=⇒ A

⁰

=B

⁰

= 1