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?