# EXACT equation

1. Aug 2, 2009

### @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 cant get exact equation once again
and in book answers IF for this equation is x^a-1.y^b-1
So., can any one tell me how can I solve this eq by method of inspection >>
plzzz help me!!

2. Aug 2, 2009

### Count Iblis

Re: EXACT equation !!

Why not just divide by xy?

3. Aug 2, 2009

### CentreShifter

Re: EXACT equation !!

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?