# Differential equation help

1. Jun 26, 2008

### goaliejoe35

The problem statement, all variables and given/known data

Find the particular solution of the differential equation $$xdy=(x+y-4)dx$$ that satisfies the initial condition $$y(1)=7$$.

The attempt at a solution

Ok heres my first two steps...

$$dy = \frac{(x+y-4)}{x} dx$$
$$\frac{dy}{(x+y-4)} = \frac{dx}{x}$$

Now here's where I get messed up. How can I get the x out of the side with the dy? Could someone please explain how to finish this or If I'm headed in the right direction?

2. Jun 26, 2008

### HallsofIvy

Is "separation of variables" the only way you know to solve differential equations? This is NOT a "separable" equation.

3. Jun 26, 2008

### goaliejoe35

Yea thats the only way I know how. But I'm looking at a different way now where they give you the standard equation y' +P(x)y = Q(x), but I don't quite understand it.

4. Jun 26, 2008

### konthelion

THat's a linear first-order differential equation. Usually, textbooks show the method for solving them. Try looking in your textbook.

5. Jun 26, 2008

### rock.freak667

Use a substitution of y=Vx

Last edited: Jun 26, 2008
6. Jun 26, 2008

### tiny-tim

y' +P(x)y = Q(x)

Hi goaliejoe35!

Hint: first step: get the RHS x-only:

xdy - ydx = (x - 4)dx.

Does the LHS now remind you of anything?

If so, fiddle around with it until you get something you can integrate.

If not, go back to your book and look at y' +P(x)y = Q(x) again