# Another ODE

1. Nov 22, 2009

### manenbu

Need help with solving this DE.

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

$$(x e^{\frac{y}{x}} + 2x^2 y)dy - y e^{\frac{y}{x}}dx = 0$$

2. Relevant equations

3. The attempt at a solution

Well, I don't even know where to start. It's not exact, and I can't make it exact with an integrating factor. All of this y/x in here makes me think that maybe I need to make a substitution here, but I can't just use it like that because it wouldn't work.
Any ideas?

2. Nov 22, 2009

### Staff: Mentor

I would start with v = y/x. I can't guarantee that it would work, since I haven't worked the problem, but it might be what you need to get an exact equation.

The substitution v = y/x is equivalent to y = vx, so y' = v + v'x.

3. Nov 28, 2009

### andylu224

Try using the substitution v = x/y which is equivalent to vy = x

So dx/dy = v + y*dv/dy

Give it a try and see if it works.

4. Nov 28, 2009

### manenbu

Yes it was, but I also had to make a substitution for y, missed it the first time.
Got it right now.

Thanks.

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