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