TM NGHI^E.M RI^ENG CU'A PHU.O.NG TRNH

25)

Tm nghi^e.m ri^eng cu'a phu.o.ng trnh:

^{(x+y−2)dx+ (x−y+ 4)dy = 0}

thoa' ma~n di^eu ki^e.n d^au

^{y(1) = 0}

.

(x =u−1HD gia’i:

D - a.t

y =v+ 3.

thay vao phu.o.ng trnh du.o..c:

(u+v)du+ (u−v)dv = 0

, d^ay la phu.o.ng trnh thu^an nh^at co tch ph^an t^o'ng quat la:

u

²

+ 2uv−v

²

=C

.

V^a.y tch ph^an t^o'ng quat cu'a phu.o.ng trnh ban d^au la:

^x

²

^{+ 2xy−y}

²

^{−4x+ 8y =C}