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## Homework Statement

a) Write (x

^{2}1)y'+2xy as the derivative of a product

b) Solve (x

^{2}1)y'+2xy=e

^{-x}

## The Attempt at a Solution

a) I use the product rule backwards and get

((x

^{2}+1)y)'

b) I exploit what i just found out...

(x

^{2}1)y'+2xy=((x

^{2}+1)y)'

and get...

e

^{-x}=((x

^{2}+1)y)'

integrate on both sides...

**∫e**

^{-x}dx=∫((x^{2}+1)y)'dx-e

^{-x}+C=(x

^{2}+1)y

and get that...

y=(C-e

^{-x})(x

^{2}+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?