# Integrating factor

• February 21st 2011, 11:11 PM
dmbocci
Integrating factor
I dont see how to make this into an I.F. format:

(3x^2y + 2xy + y^3)dx + (x^2 + y^2)dy = 0
• February 21st 2011, 11:23 PM
FernandoRevilla
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
• February 21st 2011, 11:28 PM
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.
• February 21st 2011, 11:36 PM
FernandoRevilla
Quote:

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
• February 21st 2011, 11:37 PM
dmbocci
Nope, still dont get it. heh sorry
• February 21st 2011, 11:48 PM
FernandoRevilla
Quote:

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