- #1
Math10
- 301
- 0
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.