Homework Help: Intergrating factor

1. Feb 1, 2010

annoymage

1. The problem statement, all variables and given/known data

(2y-6x)dx + (3x+4x2y-1)dy = 0

2. Relevant equations

3. The attempt at a solution

(3xy+4x2)dy/dx = 6xy-2y2

i'm stuck, want to find the intergrating factor, it's xy2 when i reverse from the answer :D.. give me any hint please

2. Feb 1, 2010

annoymage

or am i suppose to use special integrating factor??

3. Feb 1, 2010

Dick

Are you sure there is an integrating factor? Maybe I'm just not seeing it. But you could also try the substitution v=y/x. That should make it separable.

4. Feb 2, 2010

annoymage

yey, i got it now, there's another technique which i don't really know the details..

But to find suitable intergrating factor,

its something like

e($$1/M$$)[($$N(x,y)/dx$$) - ($$M(x,y)/dy$$)]

and is equal to xy2

and multiply both sides by the integrating factor, and will get Exact form of equation and solve it, hoho,

but maybe i need to try substituting v=y/x

5. Feb 2, 2010

HallsofIvy

Every first order differential equation has an integrating factor- it just may be hard to find!

Are you required to find an integrating factor? this equation is "homogeneous". Write it as
$$\frac{dy}{dx}= \frac{6x- 2uy}{3x+ 4x^2y^{-1}}= \frac{6- 2\frac{y}{x}}{3+ 4\frac{x}{y}}$$

Let u= y/x so that y= xu and dy/dx= u+ x du/dx and that will become a separable equation for u as a function of x. If you really want to find an integrating factor, I think that solving for u and then y and deriving the integrating factor from the solution is simplest.