Separable equations

Oct 2009
5
0
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...
 

mr fantastic

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Zeitgeist
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 \(\displaystyle C = e^{2K}\).