How can I verify the separability of a differential equation with constants?

[fluidistic]

Homework Statement

Verify that the following ODE can be reduced to an ODE of separable variables.
\frac{dy}{dx} =f(ax+by+c) where a, b and c are constants.2. The attempt at a solution
I think I must show that there exist functions g and h such that g(y)dy=h(x)dx.
I have that dy=f(ax+by+c) dx. I was at a loss. So I talked to a friend and he told me to write u=ax+by+c.
So I get dy=f(u)dx \Rightarrow y= \int f(u)dx=\frac{u-ax-c}{b}, y'=\frac{u'-a}{b}, y''=u''. I want to write f(u) as \phi _1 (x) \phi _2 (y) but I'm totally stuck.
I'd love a tip.
Thank you.

 

[LCKurtz]

You have figured out that y' = (u'-a)/b and if you plug that in for y' you get

(u'-a)/b = f(u)

Write u' as du/dx and, remembering that a and b are constants, see if you can't get the u terms and the x terms on opposite sides.

 

[sachinism]

ya lckurtz sums it up

also try looking here:http://www.tutorvista.com/math/separable-differential-equation"

 

[fluidistic]

Thank you guys, I got it.