
seperable equation
I reviewing for my final and stuck on this question.
dy/dx=y^2/x^2
here is my work
dy/y^2=dx/x^2, integrading both sides i get
1/y=1/x+c, i then multiple each side by negative 1 to get
1/y=1/xc, then multiplying by y i get
1=(1/xc)y, dividing by 1/xc i get
1/(1/xc)=y, but this is not one of the options for my solution, what am i doing wrong?

$\displaystyle \displaystyle \frac{dy}{dx}=\frac{y^2}{x^2}\Rightarrow \int\frac{dy}{y^2}=\int\frac{dx}{x^2}\Rightarrow \frac{1}{y}=\frac{1}{x}+C\Rightarrow $
$\displaystyle \displaystyle \frac{1}{\frac{1}{y}}=\frac{1}{\frac{1+xC}{x}}\Rightarrow y=\frac{x}{xC1}$