I was helping someone today on a basic Differential Equations problem and the answer I got disagreed with the one given in the back of the book. I'm hoping someone can confirm which is correct:

The problem is:

dy/dx = y/x

The answer I got (after combining all constants into K) is:

y = K|x|

The answer in the back of the book is:

y = Kx

(NOTE: There were no initial limits put on the domain or range of the function.)

I'm pretty sure the book "cheated" and decided to drop the absolute value (assuming the + and - would be absorbed into the K).

Can someone confirm whether that's legal to do?