Zill DE text says (y-x)dx+(4xy)dy=0 can be rewritten as....

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The differential equation (y-x)dx+(4xy)dy=0 can be rewritten as 4xy' + y = x, as stated in the Zill Differential Equations text. The user initially derived 4xyy' + y = x, which is a correct manipulation but not the simplified form presented in the text. The discussion confirms that the original equation can be transformed correctly, suggesting a possible typo in the textbook.

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Zill DE text says (y-x)dx+(4xy)dy=0 can be rewritten as:

4xy'+y=x

Am I missing something? I got 4xyy'+y=x instead.

Very rarely have I ever required starting a thread in a forum to resolve something as seemingly trivial as this but I just want to verify whether this is a typo or not.

Here are the steps I took:

The original is: (y-x)dx+(4xy)dy = 0

From there I got:

(4xy)dy=(x-y)dx

then

(4xy)dy/dx = x-y

then

(4xy)y'+y=x or 4xyy'+y=x
 
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Your reasoning looks correct. Perhaps the text has a typo.
 

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