I have the function $y=y(x)$ with $y'=dy/dx$, and the following equation: $ky'=\pm\sqrt{k^{2}-y^{2}}$, where $k$ is constant.
Integrating this, given that $y(0)=0$, should give: $y=k\sin(x/k)$.
I don't know how such an integration was calculated and how we arrived at this result. Any help explaining the integration process would be appreciated.
Many thanks.