# Homework Help: Bernoulli's o.d.e

1. Feb 18, 2010

### Mechdude

1. The problem statement, all variables and given/known data
$$\frac{dy}{dx}= - \frac{c}{n} y^{n}$$

2. Relevant equations

$$y' + p(x)y=q(x) y^n$$

3. The attempt at a solution
im strictly speaking able to do it , i just wanted to kno whether im on the right track using bernoulli's equation, not that i can see any other methods!
;-)
cheers

2. Feb 18, 2010

### rock.freak667

If c and n are constants then you can just divide by yn and you'd have a separable ODE

3. Feb 18, 2010

### Mechdude

thanks , i try that ( c and n are constants). seems less involving if not actually suggesting i was on the wrong track

4. Feb 18, 2010

### LCKurtz

I don't think you will find it to be separable. Bernoulli's method is the way to go. Dividing by yn puts it in the form

y(-n)y' +p(x)y(1-n)= q(x)

and the change variable v = y(1-n) transforms it into a linear first order equation which can be done with an integrating factor.

 Correction -- your specific equation is indeed separable, it is the general Bernoulli equation that isn't.

Last edited: Feb 18, 2010
5. Feb 18, 2010

### Mechdude

i did find it to be separable and got an expression for a problem im working on that agrees with the solution provided, so im confident about that . thanks though.

here's the source of the d.e. for the curious :