A) TM MI^EN MA TRONG DO NGHI^E.M CU'A BAI TOAN CAUCHY CU'A PHU.O.N...

63)

a) Tm mi^en ma trong do nghi^e.m cu'a bai toan Cauchy cu'a phu.o.ng trnh sau

d^ay t^on ta.i va duy nh^at

^y

⁰

^{=y+ 3x.}y”− 1

b) Tm nghi^e.m cu'a bai toan Cauchy sau d^ay

xy

⁰

=xy(x= 1) = 1 va` y

⁰

(x= 1) = 2.HD gia’i:

a) D - ^ay la phu.o.ng trnh tuy^en tnh c^ap 1 tho'a di.nh ly di^eu ki^e.n t^on ta.i duy nh^at

nghi^e.m tr^en

^R

²

^.

b) Gia'i phu.o.ng trnh

^{y”− y}

⁰

x =x

, ta du.o..c nghi^e.m t^o'ng quat

y =C

₁

+C

₂

x+ x

²