Non-linear ODE: y'=(y-1)^2 + 0.01

[CINA]

Homework Statement

y' = ( y - 1 )^2 +0.01 y(0)=1


(trying out latex)
$$y' = (y-2)^{2} + 0.01; y(0)=1$$

Homework Equations

Separation of variables, Right?

The Attempt at a Solution

The solution is is y(x)=1+0.1 Tan (0.1x)

How did they get this? I did separation of variables and got:

dx = ( 1/(y-1)^2 + 100 )dy

integrating gets:

x = -1/(y-1) +100y + C

Tangent...is not here. What am I doing wrong here?

 

[vela]

Check your algebra. You're making a very elementary mistake.