# Homework Help: 1st order, non linear, homogeneous, ODE

1. Oct 13, 2008

### Schmoozer

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

"Solve the following ODE's:"
"3u+(u+x)u'=0"

This is our first weeks homework and he went this through this so quickly in class.

2. Relevant equations

None. x and u are both variables.

3. The attempt at a solution
I know it is homogeneous and non linear. I tried v-substitution and just couldn't get a v to fit. Do i need to use the method of integration factor?

Thanks guys!

Last edited: Oct 13, 2008
2. Oct 13, 2008

### Defennder

Why doesn't this work? What do you understand by v-substitution?

3. Oct 13, 2008

### Schmoozer

Not much, I feel like I'm guessing... any suggestions what i should substitute?

4. Oct 13, 2008

### HallsofIvy

Perhaps better to rewrite it as
$$u'= \frac{-3u}{u+x}= \frac{-3\frac{u}{x}}{\frac{u}{x}+ 1}$$

5. Oct 13, 2008

### Schmoozer

-(1/4)ln|(u/x)|=ln|x|+c ?

Thanks so much. This class is like diffy eq on steroids and wasn't very good at diffy eq.