Consider the differential equation(adsbygoogle = window.adsbygoogle || []).push({});

dx+ydy=0, the integration leads to (x2-x1)+(y2^2-y1^2)/2=0 (1)

Suppose we know that y/x = const.

Lest proceed to the following manipulation on the initial equation, by dividing by (x), then

dx/x+(y/x)dy=0, now the integration gives ln(x2/x1)+(y/x)*(y2-y1) (2)

Correct? Well solutions (1) and (2) are different, i.e. for the same set of x1,x2,y1 they give different values of y2.

Where is the mistake?

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# Dividing differentials

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