Differential Equation (First order with separable variable) Given that $\frac{dy}{dx}=xy^2$. Find the general solution of the differential equation. 
My attempt, 
$\frac{\frac{dy}{dx}}{y^2}=x$
$\int \frac{\frac{dy}{dx}}{y^2} dx=\int x dx $
$-\frac{1}{y}=\frac{x^2}{2}+c$
$y=-\frac{2}{x^2+2c}$
Why the given answer is $y=-\frac{2}{x^2+c}$? What did I do wrong?

The constant is arbitrary. You can equally well have $3c,-c$, or even a different letter, like $A$; they are all equivalent. The given answer has just chosen a simpler-looking form.
