GIA'I PHU.O.NG TRNH

36)

Gia'i phu.o.ng trnh:

^y

⁰

^{+ 1}2x−y

²

= 0HD gia’i:

Coi

^x=x(y)

la ham cu'a

^y

ta co:

^y

⁰

^{= 1}x

⁰

thay vao phu.o.ng trnh:

1x

⁰

+ 12x−y

²

= 0⇔x

⁰

+ 2x=y

²

:

phu.o.ng trnh tuy^en tnh.

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

^x=Ce

^−2y

Bi^en thi^en hang s^o:

^C

⁰

^{(y) = y}

²

^e

^2y

^{⇒C(y) = 1}2y

²

e

^2y

−12ye

^2y

+ 14e

^2y

+C

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

^x=Ce

^−2y

⁺¹₂^y

²

^{− 1}₂^y+1₄