What Is the Correct Integrating Factor for the Equation ay dx + bx dy = 0?

[@m@]

EXACT equation !

hi! to all
I want little help about exact equation..
that the given equation is
>> ay dx + bx dy= 0
I had solved and found integrating factor of all of my equations by formula
P(x) = My-Nx/N
but for this equation I have got IF for this equation is x((a-b)/b) and after multiplying this factor by equation I can't get exact equation once again
and in book answers IF for this equation is x^a-1.y^b-1
So., can anyone tell me how can I solve this eq by method of inspection >>
pleasezz help me!

 

[Count Iblis]

Why not just divide by xy?

 

[CentreShifter]

In order to determine what the integrating factor is you must first normalize the equation.
$$\frac{dy}{dx}+P(x)y=f(x)$$
is an example of a normalized differential equation, the IF being
$$e^{\int P(x)dx}$$.

Does this help?