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## Homework Statement

Find all solutions of xy'=2-x+(2x-2)y-xy^2.

## Homework Equations

None.

## The Attempt at a Solution

The answer in the book is y=1-1/(x(1-cx)).

Here's my work:

xy'=2-x+2xy-2y-xy^2

xy'=(xy^2-2xy+x)+2(1-y)

xy'=x(y-1)^2-2(y-1)

y'=(y-1)^2-2(y-1)/x

u=y-1

u'=y'

u'=u^2-2u/x

And now I'm stucked. Please help me, I've struggled with this problem for a long time.