# Math Help - Separable Differential Equations

1. ## Separable Differential Equations

I need help in this problem!

$dy/dx=3x^2 (y-2)^2$

I moved the dx to the other side and divided by (y-2)^2 but I got stuck in that part. I know that I have to integrate but I don't know how to continue:

$\int dy/(y-2)^2 = \int 3x^2dx$

2. Originally Posted by littlesohi
I need help in this problem!

$dy/dx=3x^2 (y-2)^2$

I moved the dx to the other side and divided by (y-2)^2 but I got stuck in that part. I know that I have to integrate but I don't know how to continue:

$\int dy/(y-2)^2 = \int 3x^2dx$
To integrate the left side, use the partial fractions method or substitute $u=y-2$ ..
the right side should be easy ..

3. So the left side would be -1/u?

4. Originally Posted by littlesohi
So the left side would be -1/u?
Yes .. which is $\frac{-1}{y-2}$ ..