# DE method problem

1. May 13, 2006

### gbacsf

What method would be used to solve this DE, it look like a Bernoulli but isn't. I'm lost.

y'cosx = 1-y^2

Thanks,

Gab

2. May 13, 2006

### neutrino

It looks like you can separate the variables.

3. May 13, 2006

### Pseudo Statistic

Treat y' as the limiting ratio dy/dx.
Your aim is to get the xs (and dx) on one side, and the ys (and dy) on the other side and integrate...

4. May 14, 2006

### gbacsf

5. May 14, 2006

Hint:

$$\frac{dy}{dx} \,\, \frac{\cos x}{1-y^2}=1$$

6. May 14, 2006

### gbacsf

Well from that I can say that y=sin(x) is a solution.

Then I get:

z' +(-2*tan(x))*z = 1/cos(x)

So then I solve this linear equation:

(sin(x) + C)/(cos(x))^2

Last edited: May 14, 2006
7. May 15, 2006

### J77

The next step should be to substitute: $$y=\sin(u)$$ into the equation FrogPad gave.