Help with Second order linear differential equation

[fugitivemotel]

am required to rewrite the following second order differential
equation:
(1+x^2)d^2y/dx^2 + 2x dy/dx = 1
in the form
d/dx (f(x)dy/dx) = 1
for some function f(x), but I have tried and tried and cannot find a
way to do it. Please can you help me.

 

[Gene]

D = dy/dx
(1+x^2)D^2 + 2xD = 1
Using the product rule
d((1+x^2)D) =
(1+x^2)D^2 + D(d(1+x^2)) =
(1+x^2)D^2 + 2xD
which is the left side of the equation. so
f(x) = 1+x^2