How in the world do I solve this differential equation?

dy/dx = x(x-y)

I've been staring at this for the past half hour, and I'm completely stumped. I can't separate the variables, but I can't integrate it in this form either. I don't know what to do.

EDIT: I feel dumb now. This is dy/dx + P(x)y=Q(x).

Am I correct in thinking that P(x) can = x?

Quote:

---

Originally Posted by MonkeySage

Am I correct in thinking that P(x) can = x?

---

Is x a function of x?

Quote:

---

Originally Posted by MonkeySage

dy/dx = x(x-y)

I've been staring at this for the past half hour, and I'm completely stumped. I can't separate the variables, but I can't integrate it in this form either. I don't know what to do.

EDIT: I feel dumb now. This is dy/dx + P(x)y=Q(x).

Am I correct in thinking that P(x) can = x?

---

My understanding is that you do this:

dy/dx = x(x-y) = (x^2) -xy

for f(y), x and x^2 are constants.

y = (x^2)y - (x/2)(y^2)

If you want y in terms of x, then divide by y on both sides and then seperate the variables.

1 = (x^2) - (x/2)y

(x/2)y = (x^2)-1

y = 2x - (2/x) or y = 2x - 2(x^-1)

I could be in error though. It's been a while since I had to do this sort of maths.