# Homework Help: Differential Equations Problem

1. Jan 24, 2010

### tomeatworld

1. The problem statement, all variables and given/known data
x y' + 3y = x2

2. Relevant equations

3. The attempt at a solution
So I tried using an integrating factor (as I couldn't seperate variables).
So I've said that the function p(x)= 1/x and q(x)=x. So the integrating factor is elog(x) or x. Putting this in:
x y = $$\int x^{2}$$ so
x y = $$\frac{1}{3} x^{3}$$ + c
and finally: y(x) = $$\frac{1}{3} x^{2} + \frac{c}{x}$$ but this isn't the right answer. Where have I gone wrong?

2. Jan 24, 2010

### Staff: Mentor

You don't have the right integrating factor. Starting from y' + (3/x)y = x, your integrating factor should be x3. Multiplying by the integrating factor gives x3y' + 3x2y = x4.

This equation can be written as d/dx(x3y) = x4. Can you take it from there?

3. Jan 24, 2010

### tomeatworld

ahh I see! yeah, that's great! thanks a load!