GIA'I PHU.O.NG TRNH X2Y” +XY0+Y=X BANG PHEP D^O'I BI^EN X=ETHD GI...

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Gia'i phu.o.ng trnh

^x

²

^{y” +xy}

⁰

^+y=x

bang phep d^o'i bi^en

^x=e

^t

HD gia’i: x=e

^t

ta co:

^y

⁰

x

=y

⁰

_t

.1x; y”

xx

= (y”

tt

−y

_t

⁰

) 1x

²

Thay vao phu.o.ng trnh:

^y”

tt

+y=e

^t

Nghi^e.m t^o'ng quat cu'a phu.o.ng trnh thu^an nh^at:

^y=C

¹

^cost+C

²

^sint

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

^y+Ae

^t

^{; A= 1}₂

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

^y=C

¹

^{cos (lnx) +C}

²

^{sin (lnx) + x}₂