Помогите решить. Высшая математика.

x y' + y = - x y^2,
(x y)' = - x y^2,
d(x y) / (x y)^2 = - dx / x,
-1 / (x y) = C - ln|x|,
x y = 1 / (C + ln|x|),
y = 1 / [x (C + ln|x|)].

y' + y/x = -y^2
y(x)=u*v
y'=u'v + uv'
u'v + uv' + uv/x =-(uv)^2
v(u' + u/x) + uv' = -(uv)^2
1) u' + u/x = 0
du/u = -dx/x
lnu =-lnx;
u=1/x
2) uv' = u^2 * v^2
dv/dx=-(v^2)/x
dv/(v^2) = -dx/x
(v^-1) / (--1) =- (lnx + lnC)
1/v=ln(Cx)
v=1/[ln(Cx)]
решение:
y=u*v=(1/x) * 1/[ln(Cx)]=1/[x*ln(Cx)]