Hi!
I have problem solving this equation
dy/dx = y/2x
The answer should be y^2 = Cx
I cannot understand why you multiply the constant with x...
$\displaystyle \frac{1}{y} \, dy = \frac{1}{2} \int \frac{1}{x} \, dx$.
Therefore $\displaystyle \ln |y| = \frac{1}{2} \ln |x| + K = \ln (\sqrt{x}) + K$
$\displaystyle \Rightarrow y = \sqrt{x} e^K$
$\displaystyle \Rightarrow y^2 = x e^{2K} = C x$ where $\displaystyle C = e^{2K}$.