GIA'I PHU.O.NG TRNH

109)

Gia'i phu.o.ng trnh:

^y”−4y

⁰

^{+ 5y=e}

^2x

^{+ cosx}HD gia’i:

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

^λ

²

^{−4λ+ 5 = 0⇔λ}

¹

^{= 2−i;λ}

²

^{= 2 +i}

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

^y=e

^2x

^(C

¹

^cosx+C

²

^sinx)

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

^{y = y}

¹

^+y

²

vo.i

^y

¹

^{= Ae}

^2x

^{; y}

²

^{= Acosx+Bsiny ⇒ y}

¹

⁼e

^2x

; y

2

= 18cosx−18sinx

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

^y=e

^2x

^(C

¹

^cosx+C

²

^{sinx) +e}

^2x

⁺¹₈^{(cosx−sinx)}