Bernoulli Differential equations?

Question

I need to solve these 2 questions:

1. Find the solution to the following diff. equation
(x+y)dy/dx + y = 0
the answer should be y^2+2xy=C

2. Wich is the solution to the following differential equation?
dy/dx - (1/x)y = -xy^2
the answer should be x/(2x^2 + C)

I tried working them according to what the book shows me but get stuck. I used Q(x)= -x P(x)= -1/x
let n = 2

Who can help?

Answer 1

the 1st one is simple
(x+y) dy/dx + y =0
or xdy/dx + ydy/dx + y =0
or (xdy/dx + y) + ydy/dx = 0
xdy/dx + y = d/dx(xy)

and d(y^2/2)/dx

so d/dx(xy+y^2/2) = 0

or xy+y^2/2 = c
or 2xy+y^2 = 2c or C

proved
for the second one

dy/dx -(1/x)y = xy^2

let y/x = t
y = xt
dy/dx -y/x = t+ x dt/dx -t = x dt/dx
so
x dt/dx = - x (xt)^2
or dt/dx = x^2t^2
dt/t^2 = x^2 dx
you should be able to proceed

Answer 2

Bernoulli:http://en.wikipedia.org/wiki/Bernoulli_differential_equation