GIA'I PHU.O.NG TRNH VI PH^AN

174)

Gia'i phu.o.ng trnh vi ph^an:

^x

²

^(x+ 1)y” = 2y

bi^et m^o.t nghi^e.m

^y

¹

^{= 1 + 1}_x

.

HD gia’i:

D - u.a phu.o.ng trnh v^e:

^y

⁰⁰

^{− 2}x

²

(x+ 1).y = 0;p(x) = 0;f(x) = 0.

Tm NR da.ng

Z x

²

y

₂

= (1 + 1x)(x+ 1)

²

.e

⁻

^R

^0dx

dx= (1 + 1x)(x−2 ln|x+ 1| − 11 +x)=x+ 1− x+ 1x.x ln(x+ 1)

²

− 1

V^a.y nghi^e.m t^o'ng quat: y =

^C

¹

^{(1 +} _x^{1) +C}

²

^(x−_x^{1 −1 + x+ 1}_x ^{ln(x+ 1)}

²

^{+ 1).}