- #1
Saladsamurai
- 3,020
- 7
Homework Statement
Find implicit and explicit solution for
[tex]x^2\frac{dy}{dx}=y-xy[/tex] when y(-1)=-1
So far I have:
[tex]\frac{(1-x)}{x^2}dx=dy/y[/tex]
[tex]\Rightarrow x^{-2}(1-x)dx=\ln y+C[/tex]
[tex]\Rightarrow (x^{-2)-x^{-1})dx=\ln y+C[/tex]
[tex]\Rightarrow -\frac{1}{x}-\ln x=\ln y+C[/tex]
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