A) CHU.NG MINH RANG H^E. CAC VECTO.{E2X, XE2X, X2} LA H^E. D^O.C L...

31)

a) Chu.ng minh rang h^e. cac vecto.

^{e

^2x

^{, xe}

^2x

^{, x}

²

^}

la h^e. d^o.c l^a.p tuy^en tnh.

b) Tm tch ph^an t^o'ng quat cu'a phu.o.ng trnh sau:

^{(x−y)dy−(x+y)dx= 0;}HD gia’i:

a) Dung di.nh ngh~a ki^e'm tra h^e. d^o.c l^a.p tuy^en tnh .

b) D - u.a phu.o.ng trnh v^e da.ng

^y

⁰

^{= x}_x⁺₋^y_y

. D - ^ay la phu.o.ng trnh da'ng c^ap, ta da.t

z= yx

. Khi do phu.o.ng trnh tr^en tro.' thanh

xz

⁰

= 1 +z

²

1−z .

Gia'i phu.o.ng trnh nay ta du.o..c

px

²

+y

²

=Ce

^arctg

^y

^x

.