another problem just want to check im doing it right?

....solve differential equation leaving unknown letter K in constant

$\displaystyle \frac{dy}{dx}=ky$

dy = ky dx

$\displaystyle y = \int ky + dx$

$\displaystyle =k\frac{y^2}{2} dx$

$\displaystyle \frac{1}{2}Ky^2 +C$