# Homework Help: Solving some ODEs

1. Dec 4, 2012

### Zondrina

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

Couple of ODE's I'm having trouble with, a bit rusty. They're all first orders.

(1) y' - y = -y3
(2) http://gyazo.com/4a83c6f72c552d1679b9bf95f644599c

2. Relevant equations

Substitution, integrating factors.

3. The attempt at a solution

I'm not quite sure how to go about solving the first one, integrating factors don't work, separation is obviously not happening. I highly doubt that advanced methods like the method of successive approximations is needed. Any pointers on this one would be nice.

The second one is tricky, I'm trying to turn it into a homogeneous equation so I can make the substitution v = y/x and go from there. I'm just having a bit of trouble putting it in the required form. I tried dividing by a few things like xy, x, etc, but to no avail.

Why are first orders harder than nth orders....

2. Dec 4, 2012

### Dick

Start with the first one. Why do you think separation isn't happening. It's happening for me.

3. Dec 4, 2012

### Zondrina

Wow, that's what I get for being sloppy. Just added y to both sides then divided through. Easy stuff. Simple partial fraction afterwards.

The second one though?

4. Dec 4, 2012

### Dick

You are missing the easy stuff. The right side is a function of y/x. Maybe try the substitution z=y/x.

5. Dec 4, 2012

### Zondrina

I realized I could separate it into :

$1 + \frac{y}{x} + (\frac{y}{x})^{2}$

The rest is... straightforward to say the least.

Thank you very much for the refresher, sometimes the easiest things are also easy to forget.

6. Dec 4, 2012

### Dick

No problem. Actually nth orderers are much harder. It just seems that way because they are so much harder they are usually stuck with giving easier examples.

7. Dec 4, 2012

### Zondrina

I feel with nth orders and systems of eqs there is a wide variety of well defined methods to solve a wide class of problems. It becomes systematic after second orders, i.e variation, undetermined, laplace, etc.

First orders slipped my mind pretty hard.