BANG CACH DA.T Y=UX, HA~Y GIA'I PHU.O.NG TRNH

12)

Bang cach da.t

^y=ux

, ha~y gia'i phu.o.ng trnh:

^{xdy−ydx−px}

²

^−y

²

^{dx = 0. (x >0)}HD gia’i:

D - a.t

^{y = ux;du =udx+xdu}

thay vao phu.o.ng trnh va gia'n u.o.c

^x

:

^xdu−√1−u

²

dx= 0

. Ro~ rang

^{u− ±1}

la nghi^e.m. khi

^{u6≡ ±1}

du.a phu.o.ng trnh v^e tach bi^en:

du1−u

²

= dxx

. TPTQ:

^{arcsinu−lnx=C}

(do

^{x >0}

).

V^a.y NTQ cu'a phu.o.ng trnh:

^{y=±x; arcsiny}_x ^{= lnx+C}

.