1. The problem statement, all variables and given/known data a) Write (x21)y'+2xy as the derivative of a product b) Solve (x21)y'+2xy=e-x 3. The attempt at a solution a) I use the product rule backwards and get ((x2+1)y)' b) I exploit what i just found out... (x21)y'+2xy=((x2+1)y)' and get... e-x=((x2+1)y)' integrate on both sides... ∫e-xdx=∫((x2+1)y)'dx -e-x+C=(x2+1)y and get that... y=(C-e-x)(x2+1)-1 this is the correct answer according to the book. What i am curious about is in the step marked with bold text. I wrote dx at the end just by guessing. Why couldnt i just have written dy instead?