- #1

lillybeans

- 68

- 1

## Homework Statement

(3y

^{4}-11x

^{2}y

^{2}-28x

^{4})dx-(4xy

^{3})dy=0

## Homework Equations

My=Nx if equation is exact, if not, I can make it exact (I hope) by finding an integrating factor. The problem is I can't get the integrating factor to be a function of x or y only.

## The Attempt at a Solution

Let stuff in front of dx=M

Let stuff in front of dy=N

My=12y

^{3}-22x

^{2}y

Nx=-4y

^{3}

My-Nx=16y

^{3}-22x

^{2}y

First try (My-Nx)/N=(16y

^{3}-22x

^{2}y)/4xy

^{3}

Not a function of x only.

Then (My-Nx)/-M=16y

^{3}-22x

^{2}y/-(3y

^{4}-11x

^{2}y

^{2})

Not a function of y only.

Am I using the wrong method to solve this question? I don't see any other way to go about it rather than turning this into an exact equation. Why can't I find an integrating factor that has a pure x or y expression?

Thanks.