I Integral confusion for a simple Differential Equation

anthraxiom
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Say there is a function y where dy/dx=y/x. Now if we rearrange we get dy/y= dx/x. integrating both sides, we get lny=lnx. , x=y
I simply don't know where I'm going wrong in this. lets for example say y=2x. dy/dx=y/x=2
now if we look at only the differential equation we see that dy/y=dx/x, solving we get x=y
I have no idea how this is happening, please , if possible guide my foolish thoughts to where I have gone wrong.
 
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You are forgetting the constant of integration. <br /> \int \frac{dy}{y} = \int \frac{dx}{x} \Rightarrow \ln |y| = \ln |x| + \ln |A| \Rightarrow y = Ax.
 
pasmith said:
You are forgetting the constant of integration. <br /> \int \frac{dy}{y} = \int \frac{dx}{x} \Rightarrow \ln |y| = \ln |x| + \ln |A| \Rightarrow y = Ax.
thanks :D
 
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