Integrating factor

**dmbocci** · February 21st 2011, 10:11 PM

I dont see how to make this into an I.F. format:

(3x^2y + 2xy + y^3)dx + (x^2 + y^2)dy = 0

**FernandoRevilla** · February 21st 2011, 10:23 PM

Your equation $Pdx+Qdy$ satisfies:

$\dfrac{1}{Q}\left( \dfrac{\partial P}{\partial y}-\dfrac{\partial Q}{\partial x}\right)=3$

This means that the equation has an integrating factor that depends on $x$ .

Fernando Revilla

**dmbocci** · February 21st 2011, 10:28 PM

I came up with 3, although I thought that I was looking for an x or some variable as an answer. How does that show that it depends on x. I dont quite understand.

**FernandoRevilla** · February 21st 2011, 10:36 PM

Originally Posted by dmbocci

I came up with 3, although I thought that I was looking for an x or some variable as an answer. How does that show that it depends on x. I dont quite understand.

$3=3+0x$

Fernando Revilla

**dmbocci** · February 21st 2011, 10:37 PM

Nope, still dont get it. heh sorry

**FernandoRevilla** · February 21st 2011, 10:48 PM

Originally Posted by dmbocci

Nope, still dont get it. heh sorry

$\dfrac{\mu'(x)}{\mu (x)}=3 \Rightarrow\log |\mu(x)|=\int 3\; dx\Rightarrow \ldots$

Fernando Revilla

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