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

1. Aug 31, 2010

### CINA

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

Separation of variables, Right?

3. 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?

2. Sep 1, 2010

### vela

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