Solving x^2 dy/dx = y-xy with y(-1)=-1

[Saladsamurai]

Homework Statement

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

 

[Ben Niehoff]

Actually,

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

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

 

[Saladsamurai]

Oh, yes, that looks like it would clear up the problem. Thanks Ben. The integration looked a little to easy to be getting the best of me. It's always the details...

Thanks,
Casey