Separable equations

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• May 22nd 2010, 11:26 PM
Fredrik373
Separable equations
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...
• May 23rd 2010, 12:54 AM
mr fantastic
Quote:

Originally Posted by Fredrik373
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...

$\frac{1}{y} \, dy = \frac{1}{2} \int \frac{1}{x} \, dx$.

Therefore $\ln |y| = \frac{1}{2} \ln |x| + K = \ln (\sqrt{x}) + K$

$\Rightarrow y = \sqrt{x} e^K$

$\Rightarrow y^2 = x e^{2K} = C x$ where $C = e^{2K}$.