Question

Determine correct integrating factor: dy/dx-(2x)/(1+x^2)y=2x.
I got so far and got stuck.
-1dy/dx+2xy-xdy/dx=-(2x)(1+x^2)
Sorry such a long problem.

Answer 1

First, what do you observe about 2x and (1+x^2)?

So first multiply this equation by u = 1/(1+x^2)

Then you will see that that LHS = y'/(1+x^2) + - 2x/(1+x^2)^2 = (yu)'

Answer 2

:)

Answer 3

LHS?

Answer 4

Does this clear up the confusing left side of the equation also? The u and du on right was ok, but left side seems wrong.