Trouble with Late Friday Night Homework

[erok81]

Homework Statement

I have no clue why I am having trouble with this...late friday night homework maybe.

Solve: $$y'=\frac{1}{2}(y-1)^{2}$$
y(0)=2

Homework Equations

The Attempt at a Solution

I tried variable separation and integrating from there:

$$\frac{y'}{(y-1)^{2}}=\frac{1}{2}$$

I'm not sure why that didn't work, but I couldn't get the correct from that.Any ideas?

 

[Char. Limit]

Multiply both sides of that equation by dx and it should be a very simple integral... Just make sure you get all of your signs correct.

EDIT: Although the second equation should be (y-1) and not (y-2).

 

[erok81]

Oh yes, that was a typo - thank you

I'll give it another go. For some reason after integrating it didn't look right so I gave up too soon. I am pretty sure my error is in the algebra at the end.

 

[Char. Limit]

Oh yes, that was a typo - thank you

I'll give it another go. For some reason after integrating it didn't look right so I gave up too soon. I am pretty sure my error is in the algebra at the end.

If you show your algebra, I might be able to help you.