Transform the equation into a separable differential equation:
[tex] \frac{dx}{x} = \frac{dy}{2y} \\ \frac{1}{2} lny=lnx + C \\ ln \sqrt{y} =lnx +C[/tex]
To get rid of the logarithmic terms, raise the terms to the exponential power:
[tex] e^{(ln \sqrt{y}) } = e^{(lnx + C)} [/tex]
Since [tex] e^{lnx} =x[/tex],
[tex] \sqrt{y} =x + C[/tex] since [tex] e^{C} [/tex] can be considered another constant. Squaring the whole answer gives the final answer,
[tex]( \sqrt{y} = X + C) ^{2} \\ y = x^{2} + 2Cx + C^2[/tex]
