Hi ! So I'm having trouble with a problem asking to find the integrating factor of this equation :

So my approach was to set the right-hand side to 0 to get a homogeneous DE and then use separation of variables.

This got me :

So the general solution to the inhomogeneous one with u as integrating factor is : x=

But plugging this into the original equation I arrive at :

Which I don't know how to integrate and doesn't look like it can be any of the answers I was offered (multiple-choice test).

Where did I go wrong ?

Thank you for your help !