# Again Sep of Vars

1. Feb 1, 2008

1. The problem statement, all variables and given/known data
Find implicit and explicit solution for

$$x^2\frac{dy}{dx}=y-xy$$ when y(-1)=-1

So far I have:

$$\frac{(1-x)}{x^2}dx=dy/y$$

$$\Rightarrow x^{-2}(1-x)dx=\ln y+C$$

$$\Rightarrow (x^{-2)-x^{-1})dx=\ln y+C$$

$$\Rightarrow -\frac{1}{x}-\ln x=\ln y+C$$

With the initial values, (-1,-1) are outside of the domain. What gives? My integration looks good to me. What am I missing?

Thanks,
Casey

2. Feb 1, 2008

### Ben Niehoff

Actually,

$$\int \frac{du}{u} = \ln |u| + C$$

Assuming everything else is correct, that might be your mistake.

3. Feb 1, 2008