Differential equation- putting it into form

Question

Okay, so I need to put xy' -2y=x^2 into the standard for for differential equations (y' +P(x)y=Q(x) ), and I rearranged it as y' -2y = x, but the book shows that it needs to be y' +(-2/x)y = x.
How did they get there?
Thanks!!

Answer 1

xy' -2y=x^2

 

Divide through by x:

y' + (-2/x)y = x

 

When you divided by x, you didn't divide the y term by x, which resulted in what you got.

When you divide that term by x, the result is correct.